SOLUTION: Hello! I am stuck! I am to find all the solutions in the complex number set of Z^5=-32 It has a real solution of -2 but also has 4 complex solutions. so using the euler eq

Question 781799: Hello!
I am stuck! I am to find all the solutions in the complex number set of Z^5=-32
It has a real solution of -2 but also has 4 complex solutions.
so using the euler equation I came up with
z= |z|cos5θ + isin5θ
so -2 = 2 cos5θ + isin5θ
I'm not sure how to get the solutions from this equation. I know it's easy to see if graphed, but I cannot figure out where to start.
thanks
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
It has a real solution of -2 but also has 4 complex solutions.
so using the euler equation I came up with
z= |z|cos5θ + isin5θ
so -2 = 2 cos5θ + isin5θ
--------------
z^5 + 32 --> 32cis(t), t = 0 + n*360, n = 0,1,2,3,4
Zeroes at 2cis(t/5)
--> 2, 2cis(72), 2cis(144), 2cis(216), 2cis(288)

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