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Math Help - Complex roots in conjugate pairs

  1. #1
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    Complex roots in conjugate pairs

    Given that p+iq, where p and q are real and q\neq 0, is a root of the equation
    a_0 z^n+a_1 z^{n-1}+...+a_n
    where a_0, a_1, ..., a_n are all real, prove that p-iq is also a root.

    This is the first part of the question, its the harder part. Second part is about finding constants from roots, two of which are complex.
    How do I start? I know its true, but how do I prove it?
    Thanks
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  2. #2
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    Quote Originally Posted by arze View Post
    Given that p+iq, where p and q are real and q\neq 0, is a root of the equation
    a_0 z^n+a_1 z^{n-1}+...+a_n
    where a_0, a_1, ..., a_n are all real, prove that p-iq is also a root.

    This is the first part of the question, its the harder part. Second part is about finding constants from roots, two of which are complex.
    How do I start? I know its true, but how do I prove it?
    Thanks
    http://en.wikipedia.org/wiki/Complex...e_root_theorem
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