Need Help with nth root property

Hi, I have a difficult problem with my trig homework and I'm hoping someone can help walk me through. this is the problem, thanks

I. Solve using the nth root property

(X)^5 -32i

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Originally Posted by TacticalPro

I. Solve using the nth root property
(X)^5 -32i

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Do you want the five fifth roots of

In "polar form", 32i= 32(cos(pi/2)+ i sin(pi/2))= 32e^{pi/2}.

The fifth roots of that are (32)^{1/5}(cos((pi/2+ 2npi)/5)+ i sin(pi/2+ 2npi)/4))= (32)^{1/5}e^{(pi/2+ 2npi)/5} and taking n= 0, 1, 2, 3, 4 will give the 5 different roots.