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 Do you want the five fifth roots of $\displaystyle 32\mathif{i}\text{ or } -32\mathif{i}~?$
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.
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