Complex Numbers as Vector Rotations

In this video I illustrate how complex numbers can be interpreted as vector rotations. This follows from my earlier video on equating the Rotation Matrix as a complex number. Rotating a vector by 0° is equivalent to multiplying the vector by the Identity Matrix [I]. Rotating a vector by 90° is equivalent to multiplying the vector by the Imaginary Matrix [i]. This is quite amazing, both in that complex numbers can be interpreted as vector rotations and also in that the imaginary unit i can be viewed as a 90° rotation!

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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