File:Exponentials of complex number within unit circle.svg

From Wikimedia Commons, the free media repository
Jump to navigation Jump to search

Original file ‎(SVG file, nominally 591 × 590 pixels, file size: 25 KB)

Captions

Captions

exponentials of a complex number A = 0.5 + 0.75j within unit circle

Summary

[edit]
Description
English: Exponentials of a complex number within unit circle.
Français : Les 10 premières puissances d'un nombre complexe se trouvant à l'intérieur du cercle trigonométrique et dans le premier quadrant.
Date
Source Own work
Author Krishnavedala
SVG development
InfoField
 
The SVG code is valid.
 
This plot was created with Matplotlib.
Source code
InfoField

Python code

Source code 
import numpy as np
from matplotlib import pyplot as plt
from mpl_toolkits.axes_grid.axislines import SubplotZero
from matplotlib.transforms import BlendedGenericTransform
plt.rcParams['svg.fonttype'] = 'none'

A = complex(.5,.75)
pows = [0]*11
real = [0]*11
imag = [0]*11
for p in range(11):
    pows[p] = A**(p)
    real[p] = pows[p].real
    imag[p] = pows[p].imag

fig = plt.figure(figsize=[8,8])
ax = SubplotZero(fig, 111)
fig.add_subplot(ax)

ax.set_aspect('equal')
ax.plot([0], [0], '-ok', markersize=8)
ax.plot(real, imag, '-ok', markersize=8)
ax.plot([-1,1], [0,0], 'ob', markersize=8)
ax.plot([0,0], [-1,1], 'or', markersize=8)

circ = plt.Circle(xy=(0,0), radius=1, linestyle='-.', fill=False, color='k')
ax.add_patch(circ)
arr = ax.annotate("",
            xytext=(0,0), xycoords='data',
            xy=(A.real, A.imag), textcoords='data', 
            arrowprops=dict(arrowstyle="-|>", linewidth=2, 
                            connectionstyle="arc3"),
            )
ax.plot(A.real, A.imag, 'x', color='b', markersize=15, markeredgewidth=3)
for p in range(11):
    ax.text(real[p], imag[p], '$A^{%d}$' % (p), size='xx-large')

for direction in ["xzero", "yzero"]:
    ax.axis[direction].set_axisline_style("-|>")
    ax.axis[direction].set_visible(True)

for direction in ["left", "right", "bottom", "top"]:
    ax.axis[direction].set_visible(False)
ax.text(0, 1.025, '$\Im$', transform=BlendedGenericTransform(ax.transData, ax.transAxes), ha='center', size='large')
ax.text(1.025, 0, '$\Re$', transform=BlendedGenericTransform(ax.transAxes, ax.transData), va='center', size='large')
ax.text(.75,.95, '$A=%.1f+j\,%.2f$'%(A.real,A.imag), size='large')

ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.set_xticks(np.linspace(-1,1,num=5))
ax.set_xticklabels(['-1','','0','','1'])
ax.set_yticks(np.linspace(-1,1,num=5))
ax.set_yticklabels(['$-j$','','0','','$j$'])
ax.grid(True, linestyle='--')
fig.savefig('ExponentielleComplexe_Puissances2.svg', bbox_inches='tight')

Licensing

[edit]
I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current15:55, 23 August 2017Thumbnail for version as of 15:55, 23 August 2017591 × 590 (25 KB)Krishnavedala (talk | contribs)User created page with UploadWizard

You cannot overwrite this file.

The following page uses this file:

Metadata

This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.

Retrieved from "https://commons.wikimedia.org/w/index.php?title=File:Exponentials_of_complex_number_within_unit_circle.svg&oldid=570358279"