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Simple complex numbers question

  1. Nov 15, 2008 #1
    1. The problem statement, all variables and given/known data
    z+(conjugate of z)^2=4


    2. Relevant equations
    z = x+iy
    (x+iy)+(x-iy)^2=4


    3. The attempt at a solution
    the solutions give (x+iy)+(x-iy)^2= x + x^2 - y^2. how do they reach that?
    I get (x+iy)+(x-iy)^2 = x + iy + x^2 -2xiy + i^2*y^2.
    I think the question is the ( conjugate of z )^2. e.g. z with the line on top of it and that squared.
    Thanks!
     
  2. jcsd
  3. Nov 15, 2008 #2

    Mark44

    Staff: Mentor

    They aren't showing all their steps.
    x + iy + (x - iy)^2 = 4
    ==> x + iy + x^2 - y^2 -i2xy = 4
    ==> x + x^2 - y^2 + i(y - 2xy) = 4
    Since the imaginary part of 4 is 0, it must be that y - 2xy = 0, or y(1 - 2x) = 0, which happens if y = 0 or if x = 1/2.

    Then x + x^2 - y^2 = 4 and (y = 0 or x = 1/2)
     
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