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 Jun 6 comment Can you explain $(1 + iX/n)^{n}$ without using e, sin, or cos? Thanks! I don't quite understand the image above: I understand the first frame represents $1 + i*\pi$, but I don't understand the following frames. I know I'm being a bit dense, but could you break frame 3 down for me into what each segment represents? Jun 5 asked Can you explain $(1 + iX/n)^{n}$ without using e, sin, or cos? May 23 comment Complex Exponents Thanks, that clears a lot of things up. I still don't quite understand why multiplication by (1+iX/N) is equivalent to rotation by X/N - do you think you could clear that up a bit for me? May 18 comment Complex Exponents See, that's exactly the part that I'm trying to understand by understanding complex exponents. Everybody just waves their hands and says "by definition" or pulls out a Taylor series, which is a proof, not a reason. I'm trying to figure out why $e^{ix}=cos(x) + i*sin(x)$. Lubos Motl's answer below helps, but if you have any extra pointers they'd be more than welcome. May 18 accepted Complex Exponents May 18 comment Complex Exponents That definitely helped me understand why A^i = x+iy implies that (x,y) describes a point on the unit circle. However, it still doesn't help me understand how x and y are found, or why e plays such a big role. Can you give me some pointers to understanding those two things? May 18 asked Complex Exponents May 18 awarded Scholar May 18 accepted How does e, or the exponential function, relate to rotation? May 18 awarded Supporter Mar 15 awarded Nice Question Mar 14 awarded Student Mar 14 asked How does e, or the exponential function, relate to rotation?