(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

When was trying to solve this problem

cos(x)=-2 I got the following answers

i ln(2 +/- sqrt(3)) + 2 pi n

n set of integers positive and negative

now I was told by a couple of people on here to add 2 pi n to my solution because before it didn't have it. At the time I didn't understand why but now I do. All I did was simply think about it as an angle and hence adding multiples of 2 pi n give valid solutions but what I don't understand is why does

http://www.wolframalpha.com/input/?i=(i^((2x)/pi)+i^((-2x)/pi))/(2)=-2

give me the solutions of

x = 2 pi n + pi - i log(2 +/- sqrt(3) ), n set of positive and negative integers ?

Now please understand I get that there are an infinite number of solutions. I completely understand this. This is the reason why when we define a function as a mathematical formula or representation that only has one output value for each input value of it's domain is false, correct? The complex logarithm is a completley valid function. So I understand there are an infinite amount of solutions I just don't understand were that other pi came from or the -i. I was woundering if somebody cuold please explain this to me. Thank You!

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Comlex Logarithms Question

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