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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
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Mar
15
awarded  Nice Question
Mar
14
awarded  Student
Mar
14
asked How does e, or the exponential function, relate to rotation?