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Homework Help: Complex equation

  1. Sep 1, 2009 #1
    1. The problem statement, all variables and given/known data


    in trying to solve 4z - 2conj(z) + i = 0

    2. Relevant equations

    3. The attempt at a solution

    the calculator spits out z = -1/2*i

    i did 4(a+bi) - 2(a - bi) + i = 0

    4a + 4bi - 2a + 2bi + i = 0

    2a + 6bi + i = 0

    i get z = -1/6*i

    did i mess up somewhere? also, are there other solutions?

  2. jcsd
  3. Sep 1, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    You are right. The calculator is wrong. It looks like it solved 4z-2z+i=0.
  4. Sep 1, 2009 #3


    Staff: Mentor

    Oftentimes it's difficult to get a solution, but simple to check. If z = -i/6, then
    [tex]4z - 2\bar{z} + i[/tex]
    [tex]4(-i/6) -2(i/6) + i = 0 [/tex]
    This shows that z = -i/6 is the solution to your equation. Similarly, you can show that what the calculator produced is not the solution.
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