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Math Help - Trigonometry Finding the nth roots of a complex number.?

  1. #1
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    Trigonometry Finding the nth roots of a complex number.?

    Trigonometry Finding the nth roots of a complex number.?

    Find the nth roots of the complex number and write each of the roots in standard form.

    I am trying to understand how to do this problem. but I just cannot figure out how the books answer comes up with 128 sqrt(2). The way I want to see it is 5sqrt(2). Then how does it go to 2sqrt(2)?

    fifth roots of 128(-1+i) = 128sqrt(2)(cos 135 deg + i sin 135 deg)

    Here is the books answer:

    http://i333.photobucket.com/albums/m400/.
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  2. #2
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    Dear robasc,

    this calculation maybe help you:

    128* \sqrt[2]2 = 2^5*2^2* \sqrt[2]2 = 2^5* (\sqrt[2]2)^5 = (2* \sqrt[2]2)^5
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