{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2cf2b249",
   "metadata": {},
   "source": [
    "(complejos)=\n",
    "# Números complejos en Python.\n",
    "\n",
    "\n",
    "Los números complejos juegan un papel predominante en en el lenguaje de computación cuántica, por ese motivo se ha creído conveniente abrir un apartado para hacer un resumen donde exponer los conocimientos que se necesitan sobre este tipo de números con la finalidad de que de esa manera se pueda entender mejor cómo funciona la computación cuántica.\n",
    "\n",
    "Además de la exposición teórica, también se utilizará python como herramienta complementaria para que de esta manera el lector pueda trabajar con este tipo de números desde el lenguaje de programación que es la base de qiskit.  \n",
    "\n",
    "Un número complejo $z$ es un número que posee una parte real y otra imaginaria, por ejemplo la siguiente expresión sería un número complejo:\n",
    "\n",
    "$$z=x+iy$$\n",
    "\n",
    "Cada una de las partes que conforman el número complejo se llaman *componentes*, la primera componente es la parte real ($\\Re(z)=x$) y la segunda la imaginaria($\\Im(z)=y$). Asi se tendrá $\\Re(1+i\\sqrt{3})=1$ y $\\Im(1+i\\sqrt{3})=\\sqrt{3}$.\n",
    "\n",
    "Hay que tener en cuenta que los números reales también se pueden considerar complejos pero sin parte imaginaria. Igualmente un número con sólo parte imaginaria, también será un número complejo.\n",
    "\n",
    "\n",
    "\n",
    "Cuando se facilita un número complejo en el formato que se ha dado anteriormente ($z=x+iy$), se dice que el número complejo está dado en *forma cartesiana* o *forma rectangular*. En computación cuántica es más frecuente dar el número complejo en *forma polar*, es decir de la siguiente manera:\n",
    "\n",
    "$$z=r\\cdot e^{i\\theta}$$\n",
    "\n",
    "donde r es el módulo del número complejo y $e^{i\\theta}$ es la fase compleja. Lógicamente cualquier número complejo puede ser expresado en uno u otro formato, para ello existen fórmulas de conversión entre estos formatos. Por ejemplo, si queremos pasar de forma cartesiana a polar se utilizarán las siguientes equivalencias.\n",
    "\n",
    "$$r=\\sqrt{x^2+y^2}$$\n",
    "$$\\theta=tan^{-1}(\\frac{y}{x})$$\n",
    "\n",
    "De manera recíproca, para pasar de polar a formato cartesiano, utilizaremos las siguientes equivalencias:\n",
    "\n",
    "$$x=r\\cdot cos\\theta$$\n",
    "$$y=r\\cdot sen \\theta$$\n",
    "\n",
    "Podemos utilizar las siguientes funciones construidas con código python para hacer estas transformaciones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "861bcfdd",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def cart2pol(x, y):\n",
    "    rho = np.sqrt(x**2 + y**2)\n",
    "    phi = np.arctan2(y, x)\n",
    "    return(rho, phi)\n",
    "\n",
    "def pol2cart(rho, phi):\n",
    "    x = rho * np.cos(phi)\n",
    "    y = rho * np.sin(phi)\n",
    "    return(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b845b38",
   "metadata": {},
   "source": [
    "```{index} cmath libreria\n",
    "```\n",
    "\n",
    "También existe la librería de python denominada <a href=\"https://docs.python.org/3/library/cmath.html\" target=\"_blank\"> cmath </a> que nos permite hacer este tipo de operaciones.\n",
    "\n",
    "Los números complejos en python se pueden generar de la dos formas que a continuación se indican."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "26f92e30",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3.5+1.2j)\n",
      "(3.5+1.2j)\n"
     ]
    }
   ],
   "source": [
    "a = 3.5\n",
    "b = 1.2\n",
    "c = a + b*1j\n",
    "print(c)\n",
    "c2 = complex(a,b)\n",
    "print(c2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24aa130f",
   "metadata": {},
   "source": [
    "Con las expresiones anteriores, hay que tener en cuenta que el número complejo $i=\\sqrt{-1}$ se representa en python mediante la letra $j$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3be464f4",
   "metadata": {},
   "source": [
    "Utilizando numpy podemos obtener la parte real y la imaginaria de los números complejos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7e2de857",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "parte real de c: 3.5\n",
      "Parte imaginaria de c: 1.2\n"
     ]
    }
   ],
   "source": [
    "print(\"parte real de c: {}\".format(np.real(c)))\n",
    "print(\"Parte imaginaria de c: {}\".format(np.imag(c)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a65396b",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Dentro del campo de los números complejos, también hay que tener en cuenta la denominada fórmula de Euler que dice lo siguientes:\n",
    "\n",
    "```{index} Euler fórmula\n",
    "```\n",
    "\n",
    "$$e^{i\\theta}=cos \\theta + i sen\\theta $$\n",
    "\n",
    "Todo número complejo tiene su representación en el plano cartesiano, como se puede ver en el siguiente gráfico:\n",
    "\n",
    "![](images\\representacion.PNG)\n",
    "\n",
    "Teniendo en cuenta esa imagen, en una representación cartesiana, la parte real, $x$, se representa en el eje de abscisas, mientras que en el de ordenadas, se representa la parte imaginaria, $y$. Si tenemos el número en coordenadas polares, el ángulo $\\theta$ de la figura, será el valor que acompaña al número i en el exponente, mientras que la longitud del segmento de la figura (r), será el valor de r.\n",
    "\n",
    "A continuación se facilita un código python que facilita la representación gráfica de un número complejo, dado en coordenadas cartesianas.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9054c336",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 750x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "def generate_figure(figsize=(2, 2), xlim=[0, 1], ylim=[0, 1]):\n",
    "    \"\"\"Generate figure for plotting complex numbers\n",
    "\n",
    "    Notebook: C2/C2_ComplexNumbers.ipynb\n",
    "\n",
    "    Args:\n",
    "        figsize: Figure size (Default value = (2, 2))\n",
    "        xlim: Limits of x-axis (Default value = [0, 1])\n",
    "        ylim: Limits of y-axis (Default value = [0, 1])\n",
    "    \"\"\"\n",
    "    plt.figure(figsize=figsize)\n",
    "    plt.grid()\n",
    "    plt.xlim(xlim)\n",
    "    plt.ylim(ylim)\n",
    "    plt.xlabel(r'$\\mathrm{Re}$')\n",
    "    plt.ylabel(r'$\\mathrm{Im}$')\n",
    "\n",
    "def plot_vector(c, color='k', start=0, linestyle='-'):\n",
    "    \"\"\"Plot arrow corresponding to difference of two complex numbers\n",
    "\n",
    "    Notebook: C2/C2_ComplexNumbers.ipynb\n",
    "\n",
    "    Args:\n",
    "        c: Complex number\n",
    "        color: Color of arrow (Default value = 'k')\n",
    "        start: Complex number encoding the start position (Default value = 0)\n",
    "        linestyle: Linestyle of arrow (Default value = '-')\n",
    "\n",
    "    Returns:\n",
    "        arrow (matplotlib.patches.FancyArrow): Arrow\n",
    "    \"\"\"\n",
    "    return plt.arrow(np.real(start), np.imag(start), np.real(c), np.imag(c),\n",
    "                     linestyle=linestyle, head_width=0.05, fc=color, ec=color, overhang=0.3,\n",
    "                     length_includes_head=True)\n",
    "\n",
    "c = 1.5 + 0.8j\n",
    "\n",
    "generate_figure(figsize=(7.5, 3), xlim=[0, 2.5], ylim=[0, 1])\n",
    "v = plot_vector(c, color='k')\n",
    "\n",
    "plt.text(1.5, 0.8, '$c$', size='16')\n",
    "plt.text(0.8, 0.55, '$|c|$', size='16')\n",
    "plt.text(0.25, 0.05, '$\\gamma$', size='16');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e4fb6a3",
   "metadata": {},
   "source": [
    "La representación mediante coordenadas polares se haría de la siguiente manera."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6370aec0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_polar_vector(c, label=None, color=None, start=0, linestyle='-'):\n",
    "    # plot line in polar plane\n",
    "    line = plt.polar([np.angle(start), np.angle(c)], [np.abs(start), np.abs(c)], label=label, \n",
    "                     color=color, linestyle=linestyle)\n",
    "    # plot arrow in same color\n",
    "    this_color = line[0].get_color() if color is None else color\n",
    "    plt.annotate('', xytext=(np.angle(start), np.abs(start)), xy=(np.angle(c), np.abs(c)),\n",
    "                 arrowprops=dict(facecolor=this_color, edgecolor='none', \n",
    "                                 headlength=12, headwidth=10, shrink=1, width=0))\n",
    "\n",
    "#head_width=0.05, fc=color, ec=color, overhang=0.3, length_includes_head=True    \n",
    "    \n",
    "c_abs = 1.5\n",
    "c_angle = 45  # in degree\n",
    "c_angle_rad = np.deg2rad(c_angle) \n",
    "a = c_abs * np.cos(c_angle_rad)\n",
    "b = c_abs * np.sin(c_angle_rad)\n",
    "c1 = a + b*1j    \n",
    "c2 = -0.5 + 0.75*1j\n",
    "\n",
    "plt.figure(figsize=(6, 6))\n",
    "plot_polar_vector(c1, label='$c_1$', color='k')\n",
    "plot_polar_vector(np.conj(c1), label='$\\overline{c}_1$', color='gray')\n",
    "plot_polar_vector(c2, label='$c_2$', color='b')\n",
    "plot_polar_vector(c1*c2, label='$c_1\\cdot c_2$', color='r')\n",
    "plot_polar_vector(c1/c2, label='$c_1/c_2$', color='g')\n",
    "\n",
    "plt.ylim([0, 1.8]);\n",
    "plt.legend(framealpha=1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c1f72b56",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "26a96926",
   "metadata": {},
   "source": [
    "\n",
    "## Otras cuastiones de los número complejos.\n",
    "\n",
    "Hay otros aspectos de los números complejos que el lector debe tener en cuenta.\n",
    "\n",
    "### Complejo conjugado.\n",
    "\n",
    "Son también números complejos que se obtienen cambiando de signo la parte imaginaria de otro número complejo. De esta manera si tenemos un número complejo $z=x+iy$, su conjugado será $z^{*}=x-iy$. Si el número complejo lo tenemos en forma polar ($z=r\\cdot e^{i\\theta}$), entonces su conjugado será $z^{*}=re^{-i\\theta}$ \n",
    "\n",
    "### Norma de un número complejo.\n",
    "\n",
    "La norma de un número complejo es el valor de r cuando éste está escrito en forma polar. Si lo tenemos escrito en formato cartesiano la norma se calcula de la siguiente manera:\n",
    "\n",
    "$$|r|=\\sqrt(x^2+y^2)$$\n",
    "\n",
    "Una forma fácil de calcular la norma elevada al cuadrado de un número complejo es multiplicando ese numero por cu conjugado:\n",
    "\n",
    "$$|z|^{2}=z^{*}\\cdot z=z \\cdot z^{*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee24c1cb",
   "metadata": {},
   "source": [
    "## Multiplicación de matrices de números complejos.\n",
    "\n",
    "En el campo de la computación cuántica es muy frecuente tener la necesidad de multiplicar matrices de números complejos, en particular cuando se tienen matrices que representan ciertas puertas lógicas, que se verán a lo largo de este trabajo.\n",
    "\n",
    "Para hacer este tipo de operaciones matriciales utilizaremos la clase de numpy denominada *matmul*, vemos a continuación un ejemplo.. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d861d1e2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.+2.j -1.+1.j]\n",
      " [ 2.+0.j  2.+1.j]]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([[complex(1,2),complex(-1,1)],[2,complex(2,1)]])\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c7d8a2b6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2. +1.j  0.5+1.j]\n",
      " [ 1. +3.j -2. +2.j]]\n"
     ]
    }
   ],
   "source": [
    "b= np.array([[complex(2,1),complex(0.5,1)],[complex(1,3),complex(-2,2)]])\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6c62aa59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-4. +3.j, -1.5-2.j],\n",
       "       [ 3. +9.j, -5. +4.j]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Multiplicamos las matrices \n",
    "np.matmul(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a92ec3cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-4. +3.j, -1.5-2.j],\n",
       "       [ 3. +9.j, -5. +4.j]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# También las podemos multiplicar de la siguiente manera\n",
    "a@b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d4a77d1",
   "metadata": {},
   "source": [
    "## Producto de Kronecker.\n",
    "\n",
    "```{index} Kronecker product\n",
    "```\n",
    "\n",
    "Este tipo de multiplicación de matrices, también es un elemento muy importante cuando se estudian dos o más qubits en la computación cuántica. Este tipo de producto se puede definir de la siguiente manera.\n",
    "\n",
    "![](images/kroneker.PNG)\n",
    "\n",
    "En concreto se tiene lo siguiente:\n",
    "\n",
    "![](images/kroneker2.PNG)\n",
    "\n",
    "Para hacer esta operación, numpy también nos facilita mucho la tarea, veamos cómo mediante el siguiente ejemplo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1bb38230",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0],\n",
       "       [1]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a=np.array([[0],[1]])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "85e9fdaa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [0]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b= np.array([[1],[0]])\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2f3d316d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0],\n",
       "       [0],\n",
       "       [1],\n",
       "       [0]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# El producto de Kronecker será\n",
    "np.kron(a,b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87ddb2ac",
   "metadata": {},
   "source": [
    "Si tuviéramos que multiplicar tres matrices con este procedimiento, lo haríamos de la siguiente manera "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ce50256c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [0]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c= np.array([[1],[0]])\n",
    "c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "059430df",
   "metadata": {},
   "source": [
    "Veamos cual sería el valor de \n",
    "\n",
    "$$c\\otimes b \\otimes a$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "3ba9c585",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0],\n",
       "       [1],\n",
       "       [0],\n",
       "       [0],\n",
       "       [0],\n",
       "       [0],\n",
       "       [0],\n",
       "       [0]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.kron(c,np.kron(b,a))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55cea63c",
   "metadata": {},
   "source": [
    "Notar que lo anterior se ha podido hacer porque el producto de Kronecker (también llamado producto tensorial) tiene la propiedad asociativa, pero no la conmutativa.\n",
    "\n",
    "## Apéndice sobre los números complejos con Python.\n",
    "\n",
    "En este apartado se va a mostrar una serie de detalles importantes para  poder trabajar con solidez y soltura los números complejos en python.\n",
    "\n",
    "La forma más rápida de definir un número complejo en Python es escribiendo su literal directamente en el código fuente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c3f0e1b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "z= 3+2j"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c81efa3",
   "metadata": {},
   "source": [
    "Aunque parece una fórmula algebraica, la expresión a la derecha del signo igual ya es un valor fijo que no necesita mayor evaluación. Cuando verifiques su tipo, confirmarás que efectivamente es un número complejo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "76961583",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "complex"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "023dd22d",
   "metadata": {},
   "source": [
    "Como bien se puede observar para que python reconozca que queremos definir un número complejo, es necesario añadir la letra \"j\" a continuación del segundo número.\n",
    "\n",
    "Veamos a continuación lo que ocurre cuando se introduce más términos en la suma."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "93b083aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(8+12j)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3+2j+5+6j+4j"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8fbc739",
   "metadata": {},
   "source": [
    "Podemos observar que python es lo suficientemente listo como para discriminar la parte real de la imaginaria y así hacer las suma correctamente. \n",
    "\n",
    "Otra forma de generar número complejos es utilizar una función incorporada en Python denominada *complex()* que se puede usar como alternativa a la forma presentada anteriormente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "89d4ccc8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3+2j)\n"
     ]
    }
   ],
   "source": [
    "z=complex(3,2)\n",
    "print(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77e4b7de",
   "metadata": {},
   "source": [
    "De esta forma, se parece a una tupla o a un par ordenado de números ordinarios. La analogía no es tan descabellada, pues como bien es sabido, los números complejos tienen una interpretación geométrica en el sistema de coordenadas cartesiano. Puedes pensar en los números complejos como número bidimensionales.\n",
    "\n",
    "La función de *complex()* de números complejos acepta dos parámetros numéricos. El primero representa la parte real , mientras que el segundo representa la parte imaginaria denotada con la letra j del literal que viste antes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7992f30d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "complex(3, 2) == 3 + 2j"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ce2c0a5",
   "metadata": {},
   "source": [
    "A la función *complex()* se le puede pasar como argumento un literal ( conteniendo la expresión de un número complejo) y python lo entenderá perfectamente (ojo, la cadena no puede contener ningún espacio en blanco)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "feccb1a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3+5j)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "complex(\"3+5j\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "734a80d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "complex"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(complex(3+5j))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1adcd14e",
   "metadata": {},
   "source": [
    "Para acceder a la parte real e imaginaria de los número complejos en python, se deberá actuar de la siguiente manera"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "80a36054",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "número complejo: (4+5j)\n",
      "parte real:  4.0\n",
      "parte imaginaria:  5.0\n"
     ]
    }
   ],
   "source": [
    "z= 4+5j\n",
    "print(\"número complejo:\",z)\n",
    "z1=z.real\n",
    "print(\"parte real: \",z1)\n",
    "z2 = z.imag\n",
    "print(\"parte imaginaria: \",z2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd5c8af2",
   "metadata": {},
   "source": [
    "Ambas propiedades son de solo lectura porque los números complejos son inmutables, por lo que intentar asignar un nuevo valor a cualquiera de ellos fallará:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "0627bb3d",
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "readonly attribute",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[25], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m z\u001b[38;5;241m.\u001b[39mreal \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m4.57\u001b[39m\n",
      "\u001b[1;31mAttributeError\u001b[0m: readonly attribute"
     ]
    }
   ],
   "source": [
    "z.real = 4.57"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "158d829b",
   "metadata": {},
   "source": [
    "El conjugado de un número complejo se puede obtener de la siguiente manera:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "4d89072d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4-5j)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z= 4+5j\n",
    "z.conjugate()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "494d92c0",
   "metadata": {},
   "source": [
    "Dado que *complex()* es un tipo de datos nativo en Python, puede conectar números complejos en expresiones aritméticas y llamar a muchas de las funciones integradas en ellas. Las funciones más avanzadas para números complejos se definen en el  <a href=\"https://docs.python.org/es/3/library/cmath.html\" target=\"_blank\"> módulo cmath </a>, que forma parte de la biblioteca estándar de python.\n",
    "\n",
    "Además de las sumas, restas, multiplicaciones y divisiones, que se realizan de forma tradicional como con otros tipos numéricos, también se permite la exponenciación tal y como se puede comprobar en los siguientes ejemplos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "d4c1f583",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.9353115958928275+15.7284438465799j)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z=4+2j\n",
    "2**z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "bdbed4b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.0581710272714924+0.48586827175664565j)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z**0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "af982e28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(21.758716390823256-156.74592048155935j)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z**z"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1aec2807",
   "metadata": {},
   "source": [
    "### Módulo cmatch\n",
    "\n",
    "Como ya se ha indicado anteriormente, este módulo permite realizar operaciones con números complejos, imposibles de hacer con las funciones que por defecto tiene definido python. Algunas de estas funcionalidades, las vamos a exponer en el presente apartado.\n",
    "\n",
    "Con este módulo podemos obtener la raíz cuadrada de números negativos, como por ejemplo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "0026e8b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1j"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import cmath,math\n",
    "\n",
    "cmath.sqrt(-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "398e8ed6",
   "metadata": {},
   "source": [
    "Para poder extraer todas las raices cuadradas debemos hacer lo siguiente"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "4e967707",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4142135623730951j"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cmath.sqrt(complex(-2.0,0.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "72fd385d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.4142135623730951j"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cmath.sqrt(complex(-2.0,-0.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c9abfed",
   "metadata": {},
   "source": [
    "Pero como podemos observar por defecto no nos devuelve todas las raíces cuadradas, es decir no vamos a poder extraer todas las raíces de una ecuación de una sola vez, como por ejemplo las del polinomio siguiente $x^4+1$. Para poder obtener todas esas raíces se utiliza el paquete denominado numpy, y se haría para este caso de la siguiente manera:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "f14ab8dc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.70710678+0.70710678j, -0.70710678-0.70710678j,\n",
       "        0.70710678+0.70710678j,  0.70710678-0.70710678j])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "np.roots([1,0,0,0,1]) # son los coeficientes del polinomio anterior"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62dc223f",
   "metadata": {},
   "source": [
    "Puede resultar útil conocer las distintas formas de números complejos y sus sistemas de coordenadas. Como se puede ver, estas distintas formas ayudan a resolver problemas prácticos como por ejemplo  encontrar raíces complejas. En consecuencia, en la siguiente sección, se profundizará más en estos detalles."
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "b1fd088a",
   "metadata": {},
   "source": [
    "### Conversión entre coordenadas rectangulares y polares.\n",
    "\n",
    "Como ya es sabido, un número complejo admite diferentes formas de representación. Una es la denominada forma binómica, que es la que se ha visto anteriormente, y otra la polar que estaría definida por el módulo del complejo ( distancia al origen) y el ángulo que se forma con el eje de abcisas, como se puede ver en la siguiente figura:\n",
    "\n",
    "![image.png](images/complejopolar.PNG)\n",
    "\n",
    "La propiedad que permite pasar un número complejo en forma binómica a forma polar es *polar*. Veamos el siguiente ejemplo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "2320ec23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.605551275463989, 0.982793723247329)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z=2+3J\n",
    "cmath.polar(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a4976e4",
   "metadata": {},
   "source": [
    "El resultado que se nos devuelve en una tupla, donde el primer elemento es el módulo del complejo y el segundo el ángulo o la fase de ese número. Estos datos se pueden obtener también de la siguiente manera:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "1b9d51ce",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "El valor del módulo es:  3.605551275463989\n",
      "La fase del número es:  0.982793723247329\n"
     ]
    }
   ],
   "source": [
    "modulo = abs(z)\n",
    "print(\"El valor del módulo es: \", modulo)\n",
    "fase = cmath.phase(z)\n",
    "print(\"La fase del número es: \", fase)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "022dcbfa",
   "metadata": {},
   "source": [
    "Para hacer la conversión inversa deberemos utilizar el método rect()*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "8848f92d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2+2.9999999999999996j)\n"
     ]
    }
   ],
   "source": [
    "z = 2+3J\n",
    "z2 = cmath.polar(z)\n",
    "z3 = cmath.rect(z2[0],z2[1])\n",
    "print(z3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d518081",
   "metadata": {},
   "source": [
    "Observar que el primer parámetro que se pasa a la función es el módulo del número complejo y de segundo la fase del mismo.\n",
    "\n",
    "Existen diferentes formatos para representar los números complejos. Algunas de estas formas, son las siguientes:\n",
    "\n",
    "* Algebraico\n",
    "\n",
    "* Geométrico\n",
    "\n",
    "* Trigonométrico\n",
    "\n",
    "* exponencial\n",
    "\n",
    "A continuación se muestra un código que sirve para ilustrar algunas instrucciones de Python para trabajar con estos formatos diferentes de números complejos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "6be37636",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3+2j\n",
      "3+2j\n",
      "3+2j\n",
      "3+2j\n"
     ]
    }
   ],
   "source": [
    "import cmath\n",
    "\n",
    "algebraic = 3 + 2j\n",
    "geometric = complex(3, 2)\n",
    "radius, angle = cmath.polar(algebraic)\n",
    "trigonometric = radius * (cmath.cos(angle) + 1j*cmath.sin(angle))\n",
    "exponential = radius * cmath.exp(1j*angle)\n",
    "\n",
    "for number in algebraic, geometric, trigonometric, exponential:\n",
    "    print(format(number, \"g\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3283175f",
   "metadata": {},
   "source": [
    "Existe una notación que se utiliza mucho dentro del mundo de la programación cuántica, y esa expresión consiste en utilizar notación exponencial, y en concreto la denominada fórmula de Euler, que dice lo siguiente:\n",
    "\n",
    "$$e^{i\\theta}=cos(\\theta)+i\\cdot sen(\\theta)$$\n",
    "\n",
    "Así por ejemplo $e^{i\\pi}=cos(\\pi)+i\\cdot sen(\\pi)=-1+0\\cdot i$. Veamos cómo expresar lo anterior, desde un punto de vista de código python\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "0ea11a6c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1+1.2246467991473532e-16j)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cmath.exp(1j*np.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "650981ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "Comprobmeos que la parte real debe ser -1 y la imaginaria 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "f14e5929",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1-0j)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cmath.cos(np.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "1637346b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.2246467991473532e-16-0j)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cmath.sin(np.pi)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
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    "## Razones trigonométricas de angulos usuales.\n",
    "\n",
    "Por último y para terminar este apartado recordemos el valor de las funciones trigonométrica de los ángulos más utilizados:\n",
    "\n",
    "![image.png](images/angulosnotables.PNG)"
   ]
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