Can someone explain if this is true or if there's anything wrong with the following logic? 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?