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Complex number and its conjugate problem help

  1. Jun 29, 2017 #1
    1. The problem statement, all variables and given/known data
    Given that a complex number z and its conjugate z¯ satisfy the equation z¯z¯ + zi = -i +1. Find the values of z.

    2. Relevant equations


    3. The attempt at a solution
     
  2. jcsd
  3. Jun 29, 2017 #2
    Hey, I think z.z-=1 but what's with the zi thing. Can you upload the picture of your question? Its not clear enough.
     
  4. Jun 29, 2017 #3

    ehild

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    Hi blckndglxy, welcome to PF.

    You have to show some attempt at solving the problem. Write z as z=x+iy, substitute into the equation z¯z¯ + zi = -i +1 and solve.
     
  5. Jun 29, 2017 #4

    ehild

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    You are not right, z.z- = |z|2, square of the magnitude of z. zi is z multiplied by i.
     
  6. Jun 29, 2017 #5

    hello there.. so z¯ = x-iy right? so i have to replace the z¯ too right? sorry i'm still new and i'm clueless with this question..
     
  7. Jun 29, 2017 #6

    ehild

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    Yes. Replace z with x+iy and z- with x-iy.
     
  8. Jun 29, 2017 #7

    Ray Vickson

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    Writing ##z = x+iy## and ##bar{z} = x - iy##, your equation becomes
    $$|z|^2 = 1 - i - zi$$.
    Can you see how the value of ##x## can be determined right away from this equation? That leaves you with the simpler problem of finding ##y##.
     
  9. Jun 29, 2017 #8

    ehild

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    The original equation is z¯z¯ + zi = -i +1. z¯z¯ is not |z|2,
     
  10. Jul 1, 2017 #9
    Thanks a lot. Well I had forgotten the fact you mentioned. Really HELPFUL!
     
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