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Thread: Prove that complex number can represented in this form

  1. #1
    Mar 2012

    Prove that complex number can represented in this form


    I'm having a bit of trouble with the following:
    Prove that if complex number z != -1 and modulus of the z is 1, then z can be represented as z = (1 + xi) / (1 - xi), where x is a real number.

    What I got so far:
    z = a + bi
    a*a + b*b = 1
    z = sqrt(1 - b*b) + bi
    Now I would guess, I have to convert that last line to the required form of z = (1 + xi) / (1 - xi), but I simply can't figure this out.


    EDIT: Solved it just a few hours after posting it
    Last edited by gurty; Mar 9th 2012 at 12:28 AM.
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