How to Divide Complex Numbers Quickly

We do an example of dividing complex numbers by multiplying by the conjugate over the conjugagte, or 1.
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[@pinedelgado4743]

I LOVE THIS!!! Complex analysis is one of my favorites on which I have lots of books in my private math library!! Though I'm admittedly more familiar with the barebone basics of CA than I am with the rest of it. Yet, I've always been intrigued by the fact that it started out with early mathematicians wanting representation for the square roots of negative integers. OMG!! WOW!!

[@imeaniguess.6963]

You know, it’s kinda off but sometimes I can be walked through an entire problem and understand it enough to replicate it. Still the major thing that stops me from replicating on my own is I always wonder,”Why though”, and there’s never an answer. 🤔 Do you ever fee like that, or do you just get know why you should use some random system at any point in time?
(Also that wasn’t in response to this video, I’m doing homework and trying to find easier ways to do things lol)