Question

find the power series for e^(ix).

Answer 1

thats an i?

Answer 2

yea. the hint is to substitute ix for x in the series for e^x.

Answer 3

Euler: e^(ix) = Cos (x) + i Sin(x)
If you know Cos(x) and Sin(x) series expansion use taylor's theorem.

Or you can just straight up apply Taylor's Theorem for e^(ix)
=1+ i x - x^2/2 -(i x^3)/6 +x^4/24 +(i x^5)/120

Answer 4

thanks!