(October 2, 2018 at 12:50 pm)Aliza Wrote:(October 2, 2018 at 12:03 pm)polymath257 Wrote: 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.
Have you checked this link?
https://proofwiki.org/wiki/De_Moivre%27s_Formula
If that doesn't help, what do you mean by "exponent in front of the cos and isin"? Because, from what I see, only r has a variable exponent.
