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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Geometry of Complex Numbers in Python" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 22, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import matplotlib.pyplot as plt\n", | |
"import numpy as np # Not really needed at this moment\n", | |
"import cmath\n", | |
"\n", | |
"%matplotlib inline" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 23, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"The original complex number Re{1} Im{2} and Length : 2.236068\n" | |
] | |
} | |
], | |
"source": [ | |
"c = 1+2j # Let's start with this\n", | |
"print(\"The original complex number Re{%d} Im{%d} and Length : %f\" % (c.real, c.imag, abs(c)))" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The length is defined as $ | a+ib | = \\sqrt{a^2 + b^2} $" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### Cartesian representation (Argand Plane) of Complex Number" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 24, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 1152x576 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"fig = plt.figure(figsize=(16, 8))\n", | |
"origin = [0], [0]\n", | |
"plt.quiver(*origin, c.real, c.imag, color=['r','b','g'], scale=21)\n", | |
"plt.axhline(0, color='black')\n", | |
"plt.axvline(0, color='black')\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### Polar representation of Complex Numbers" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 25, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"[<matplotlib.lines.Line2D at 0x11cd26f98>]" | |
] | |
}, | |
"execution_count": 25, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 1152x576 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"fig = plt.figure(figsize=(16,8))\n", | |
"plt.polar([0, cmath.phase(c)],[0, abs(c)],marker='o')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The Angle for $ a+ib $ is defined as $ \\theta = \\tan ^{ - 1}(\\frac{b}{a}) $\n", | |
"\n", | |
"Using euler identity we can get rid of the trigonmetric fucntions and write it in the following way- \n", | |
"\n", | |
"$ a+ib = \\sqrt{a^2 + b^2} * e ^ {i*\\tan ^{ - 1}(\\frac{b}{a})} $\n", | |
"\n", | |
"If we express $ r = \\sqrt{a^2 + b^2} $ and $ \\theta = \\tan ^{ - 1}(\\frac{b}{a}) $ then the above can be written as \n", | |
"\n", | |
"$ a+ib = re ^ {i\\theta} $" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 26, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"0.0\n" | |
] | |
} | |
], | |
"source": [ | |
"# Proving euler identity in Python (fun activity)\n", | |
"import math\n", | |
"print ((math.e**(math.pi*1j)).real + 1)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 27, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def rotate(number, degree):\n", | |
" n = number\n", | |
" return (math.e**(math.radians(degree)*1j)) * n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 28, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"c2 = rotate(c, 45)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 29, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 1152x576 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"fig = plt.figure(figsize=(16,8))\n", | |
"cs = c, c2\n", | |
"for c in cs:\n", | |
" plt.polar([0, cmath.phase(c)],[0, abs(c)],marker='o')" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 30, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def scale(number, scale):\n", | |
" n = number\n", | |
" return n * scale" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 31, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"After the operation Re{-1}, Im{4} and legth : 4.472136\n" | |
] | |
} | |
], | |
"source": [ | |
"c3 = rotate(scale(1+2j, 2), 45)\n", | |
"print(\"After the operation Re{%d}, Im{%d} and legth : %f\" % (c3.real, c3.imag, abs(c3)))" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The above is the double of the first one in legth $ 4.472136 = 2.236068 * 2 $" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 32, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 1152x576 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"fig = plt.figure(figsize=(16,8))\n", | |
"cs = 1+2j, c3\n", | |
"for c in cs:\n", | |
" plt.polar([0, cmath.phase(c)],[0, abs(c)],marker='o')" | |
] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.6.5" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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