Name: Euler's Formula as a Rotation Matrix
Uploaded: 2023-03-09T17:49:54+00:00
Duration: 11 min 36 s
Description: In this video I rewrite Euler's Formula to make it in the form of a rotation matrix. This follows from my earlier videos on equating complex numbers as vector rotations. Furthermore, for the case x =

1 year ago

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In this video I rewrite Euler's Formula to make it in the form of a rotation matrix. This follows from my earlier videos on equating complex numbers as vector rotations. Furthermore, for the case x = π, we get Euler's Identity, which in matrix form is just the negative Identity Matrix. Thus, even Euler's famous formula can be interpreted as simply rotating a vector. Since complex numbers are used in many areas of physics, such as electromagnetism and quantum mechanics, it may be fruitful to start reinterpreting other famous formulas as rotational matrices! In fact, this is exactly what Fractal Woman has attempted to do already: https://www.youtube.com/user/FractalWoman/search?query=complex%20numbers

The timestamps of key parts of the video are listed below:

- Reinterpreting Euler's Formula: 0:00
- Applications to Other Fields: 10:48

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