# Need Help with nth root property

• Apr 13th 2011, 12:52 PM
TacticalPro
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
• Apr 13th 2011, 12:59 PM
Plato
Quote:

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

Do you want the five fifth roots of $32\mathif{i}\text{ or } -32\mathif{i}~?$
• Apr 15th 2011, 05:52 AM
HallsofIvy
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.