Studying Mathematics Thread

[Aliza]

Yeah, they're talking a bit above my pay grade.

I had a mini-meltdown last night when I couldn't figure out why De Moivre's theorem worked. Like, why can you just take those exponents and drop them all willy nilly into the equation like that? The formula looked familiar enough, but I couldn't for the life of me remember what it was. Surely it's not so simple as Euler's formula. I would have recognized that right away. So I spent all night typing variations of "why the fuck does de moivre's theorem work?" into search engines only to realize that there was a common theme in the answers.

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It's Euler's formula.

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So yeah, their conversation is a bit over my head. But that's okay! I'm learning.

Alternatively, it is the cosine and sine sum formulas applied repeatedly by induction.

But wait... seriously... why do you just get to put the exponent in front of the cos and isin? How does that work? See, I once had this professor who insisted on proving to us why a formula worked, and I'd sit there in class thinking, "I don't give a shit! This is boring and confusing. Just give me the formula and I'll plug in my little values and get an A in your class. Cause that's what I do!"

But now I'm in this place where I'm seeing things and I can't just take DeMovire's word for it. I'll grant that I'm more inclined to take Euler's word for it, but I'd still like to know why this formula works.