File:Rotations on the complex plane.svg
From Vigyanwiki
Size of this PNG preview of this SVG file: 606 × 600 pixels. Other resolutions: 242 × 240 pixels | 485 × 480 pixels | 776 × 768 pixels | 1,035 × 1,024 pixels | 2,069 × 2,048 pixels | 785 × 777 pixels.
Original file (SVG file, nominally 785 × 777 pixels, file size: 18 KB)
Summary
| Description | Four numbers on the real line are multiplied by integer powers of the imaginary unit, which corresponds to rotations by multiples of the right angle. |
| Source |
Self-made. Written in TeX with TikZ, compiled using latex rot.tex && dvisvgm -n -c1.75 rot.dvi |
| Author | Keφr |
TeX source
\documentclass{article}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{tikz}
\usepackage{scalefnt}
\begin{document}
\pagestyle{empty}
\def\rotarc#1#2#3#4#5{
\draw[#2,fill=#2] (#1,0) circle (0.03);
\draw[#2,fill=#2] ({#1*cos(#3)},{#1*sin(#3)}) circle (0.03);
\draw[thick,->,#2] (#1,0.075) arc (asin(0.075/#1):#3/2:#1) node [anchor=#5] {#4} arc (#3/2:#3-asin(0.075/#1):#1) ;
}
\begin {tikzpicture} [scale=2]
\draw[dashed,->] (-3.1,0) -- (3.1,0) node [anchor=north] {Re} ;
\draw[dashed,->] (0,-3.1) -- (0,3.1) node [anchor=west ] {Im} ;
\rotarc {0.5} {red } { 90} {$i^1 = i$} {south west}
\rotarc {1.2} {olive } {180} {$i^2 = -1$} {south west}
\rotarc {1.9} {teal } {270} {$i^3 = -i$} {south east}
\rotarc {2.6} {blue } {360} {$i^4 = 1$} {south east}
\end {tikzpicture}
\end{document}
Licensing
I, the copyright holder of this work, hereby publish it under the following licence:
 
|
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 neighbouring 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/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 20:07, 23 October 2014 | | 785 × 777 (18 KB) | wikimediacommons>Kephir | {{Information |Description=Four numbers on the real line are multiplied by integer powers of the imaginary unit, which corresponds to rotations by multiples of the right angle. |Source=Self-made. Written in TeX with TikZ, compiled using <code>latex rot... |
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