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Math Help - Complex numbers in polar

  1. #1
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    Complex numbers in polar

    Hi All,
    I am preparing for my BCA 2nd semester examination.I came across with a mathematical question in which i am stuck please help.

    Find all the sixth roots of (12 + 5i)







    Thanks
    Arun.
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  2. #2
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    Quote Originally Posted by arunkayal View Post
    Hi All,
    I am preparing for my BCA 2nd semester examination.I came across with a mathematical question in which i am stuck please help.

    Find all the sixth roots of (12 + 5i)

    Convert to polar representation@

    (12 + 5i) = sqrt(12^2 + 5^2) exp(i*[arctan(5/12)+2*n*pi]), n= 0, +/-1, ...

    Then

    (12 + 5i)^(1/6) = (12^2 + 5^2)^(1/12) exp(i*[arctan(5/12)+2*n*pi]/6), n= 0, +/-1, ...

    of which only 6 are distinct, say n = 0. 1, 2, ..5.

    RonL
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