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Math Help - Need Help with nth root property

  1. #1
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    Angry 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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  2. #2
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    Quote Originally Posted by TacticalPro View Post
    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}~?
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  3. #3
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    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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