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Math Help - Complex Numbers

  1. #1
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    Complex Numbers

    Hi guys, need help with this question:

    Find the 2 complex numbers z1 and z2 each of which satisfies the following EQN:

    3zz* + 2(z-z*) = 39 + 12i

    To solve this, I let z = x + yi
    3zz* + 2(z-z*) = 39 + 12i
    => 3(x^2 + y^2) + 2y = 39 + 12i

    Equating Real and Imaginary parts:
    3x^2 = 39 => x = sq root 13
    3y^2 + 2y = 12 => y = (-1/3) + sq root (37/9)

    However, my ans was wrong. Any idea what went wrong? Thanks in advance!
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  2. #2
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    Assuming that you're using z* to represent \displaystyle \overline{z}, you should note that \displaystyle 2(z - \overline{z}) = 2[x+iy - (x-iy)] = 2(2iy) = 4iy.

    Fix the rest.
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  3. #3
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    _ _
    3ZZ = 3(x^2+y^2) and 2(z-z) =4iy
    therefore equating real and imaginary parts we get

    3(x^2+y^2) = 39 and 4y = 12

    y = 3 gives x = +2 & -2
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