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Solve the Complex Numbers equation

  1. Oct 21, 2014 #1
    1. The problem statement, all variables and given/known data

    Solve the following complex equation for z:

    zi = sqrt(3) - i

    2. Relevant equations

    3. The attempt at a solution

    Do I have to equate the real and imaginary parts ?, this is what I tried

    zi = (x+iy)i = exp(i*log(x+iy))
  2. jcsd
  3. Oct 21, 2014 #2


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    I suggest to use the exponential form.

  4. Oct 21, 2014 #3
    I'm not sure what form that is. I tried doing it this way but it gets very messy and I don't think it works out
  5. Oct 21, 2014 #4
    The polar, or exponential, form of a complex number is z = |z| ei arg z, did you learn that?

    Also, 2 = eln2
    Last edited: Oct 21, 2014
  6. Oct 21, 2014 #5

    Ray Vickson

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    Nevertheless, show us what you obtained, messy or not. Anyway, the answer should be messy.
  7. Oct 22, 2014 #6
    I tried it and I got up to this stage

    (|z| ei arg z)i
    = zi e-arg z
    = eI lnz e-arg z

    And, I'm stuck
  8. Oct 22, 2014 #7


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    You can do something with the other side, too. Write it in exponential form.

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