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Math Help - Complex numbers - find possible values of z

  1. #1
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    Complex numbers - find possible values of z

    This is my first post, so please don't kill me if I've missed something. Tried to look for a similar problem, but without any results.

    "Given that the complex number z and its conjugate z* satisfy the equation zz* + iz = 66 - 8i, find the possible values for z."

    The key says the answer is -8 + 2i and -8 - i.

    I would be grateful for a walktrough how to calculate this (i've come a bit on the way, however I get the imaginary part to be [-1 +- srt(7)i] / 2..)

    PS. sorry for the lack of latex, im in a hurry to a training, will update post later!
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  2. #2
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    Quote Originally Posted by mewoshh View Post
    "Given that the complex number z and its conjugate z* satisfy the equation zz* + iz = 66 - 8i, find the possible values for z."
    Let z=x+iy.
    Then z\overline{z}+iz=x^2+y^2+ix-y=66-8i
    Now solve for x~\&~y.
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