Can someone explain if this is true or if there's anything wrong with the following logic?(adsbygoogle = window.adsbygoogle || []).push({});

e^ix = cos(x) + isin(x)

Let x = pi/2 + 2npi

Then,

e^ix = i

Take both sides to the exponent i,

e^-x = i^i

e^-(pi/2 + 2npi) = i^i

But, e^(pi/2 + 2npi) has infinite different values.

I've been looking around on the internet and I can only find the typical e^(-pi/2) solution. Is it just that mathematicians have just decided to define it to be that value? Even wolfram alpha spits out only one value. Is it just as correct to say that i^i = e^-(5pi/2) for example?

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# I^i has infinite values?

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