This is a great post. I was planning to post on this, but unfortunately you beat me to the punch. Nevertheless, this is very well written. If it's ok with you, I want to build upon this and talk about the complex roots of unity, and their relation to the unit circle.
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Thank you!
I would be happy to see a post about the unity circle from you!
And don't worry, I don't think that I will talk about more in complex numbers in a post specific only for that topic.
But, I may talk about more when they are needed in something else (like signal analysis), if it wasn't already been explained in this post!