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Find all complex numbers z such that z^4 = -4. 

Note: All solutions should be expressed in the form a+bi, where a and b are real numbers.

 

I have an idea of how to solve this but I just want to see how others would solve it. Thanks!

 Mar 1, 2020
 #1
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\(z^4 = -4 = 4e^{i(2k+1)\pi},~k\in \mathbb{Z}\\ z = \sqrt{2}e^{i(2k+1)\pi/4},~k=0,1,2,3\\ z = 1+i,~-1+i,~-1-i,~1-i\)

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 Mar 1, 2020
 #2
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Thanks.

Guest Mar 1, 2020

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