Rotation Matrix is Equivalent to a Complex Number

In this video I go over a pretty amazing property of the Rotation Matrix, which is that it can be viewed as equivalent to a complex number! I show this by writing the Rotation Matrix as an addition of two matrices. The properties of the first matrix, called the Identity matrix, is similar to the real number 1. The properties of the second matrix has properties of the imaginary unit i. And the Rotation Matrix equation itself is equivalent to the complex number z = a + bi. Thus, complex numbers can be interpreted as vector rotations! This is quite the amazing property since it makes complex numbers more tangible and less "imaginary" or "complex".

This is quite the amazing property

This video was taken from my earlier video listed below:

- Complex Numbers as Rotation Matrices: https://youtu.be/Mgp2vrQeLEw
- Video notes: https://peakd.com/hive-128780/@mes/complex-numbers-as-rotation-matrices
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0E6x0dZEAx77Kqv7LLxYdbx

Related Videos:

Vectors and the Geometry of Space Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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