Analysis of $e^{ix}$ by Maclaurin Formula

[Nea]

Analyze by Maclaurin formula:
$e^{ix}$

 

[Zurtex]

Do you know the 'formula' for e^x? If so, try substituting ix for x.

 

[finchie_88]

You could also do it by looking at the power series of cosx and sinx, and then multiply the sine power series by i and then add the power series of cos on to it, so you get $cosx + isinx$. Either way will get you the same answer, and the first method would probably be a little quicker.