 Welcome back MechanicalEI, did you know that all the major functions in your mobile phone like swiping, zooming and rotation are all governed by standard transformations? This makes us wonder, what are standard transformations? Before we jump in, check out the previous part of the series to learn about what conformal mapping is. Now, consider a complex variable w equals 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 scalar 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 2 pi by 3 and 4 pi by 3 and are given by b equals to a into e power 2i pi upon 3 and c equals to a into e power 4i pi upon 3. Translation is simply shifting of the entire function along the rear or imaginary axis and is done by adding the real values and or imaginary values 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. So, like, subscribe and comment with your feedback to help us make better videos. Thanks for watching. Also, thanks a lot for those constructive comments. You helped the channel grow. So, here are the top mechanical EIs of our last videos. In the next episode of Mechanical EI, find out what Cauchy's theorem is.