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Homework Statement
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!