What are Standard transformations?
Channel: MechanicaLEi
Date: 2018-07-24

Welcome back MechanicaLEi, did you know that all the major functions in your mobile phone like swiping, zooming and rotation are governed by standard transformations? This makes us wonder, What are standard transformations? Before we jump in check out the previous part of this series to learn about what Conformal mapping is? Now, Consider a complex variable w equals to f of z. Alpha is any complex number and can be written as alpha equals to r into e power i theta then w equals to alpha into z denotes a magnification of w by a scalor factor r together with a rotation about origin O through the angle theta in anticlockwise direction. For example, If a vertex of the triangle is represented by the complex number a, the other vertex are obtained from a by rotation, about the origin, of angles two pi by three and four pi by three and are given by  b equals to a into e power two i pi upon three and c equals to a into e power four i pi upon 3. Translation is simply shifitng of the entire function along the real and or imaginary axis and is done by adding the real vlues and or imaginary vlues directly to w. For example to shift function w two units to the right and one unit down we simply add real number 2 and i to w. Hence, we first saw what rotation and magnification are and then went on to see what translation is?

In the next episode of MechanicaLEi find out what Cauchy's Theorem is?


Attributions:

Doh De Oh by Kevin MacLeod is licensed under a Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/)
Source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1100255
Artist: http://incompetech.com/

Subtle Library by Fabian Measures (http://freemusicarchive.org/music/Fabian_Measures/) is licensed under a Creative Commons Attribution licence ( https://creativecommons.org/licenses/by/4.0/)
Source: http://freemusicarchive.org/music/Fabian_Measures/Emotion_Music/Subtle_Library