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Math Help - Locus coordinates

  1. #1
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    Locus coordinates

    The complex numbers w and z is represented by P (x , y) and Q (u, v) on argand diagrams and

    w=z^2

    P moves along the line y=x-1. Find the cartesian equation of the locus of Q.

    I got expressions for u and v in terms of x and y first:

    u = x^2 - y^2
    v = 2xy

    Then I inserted the y=x-1 into the equations

    u = x^2 - x^2 + 2x - 1
    u = 2x - 1 --> x = \frac{u+1}{2}

    v = 2xy
    v = 2(\frac{u+1}{2})(\frac{u+1}{2} - 1)

    and my cartesian equation came out as

    v = u + 1

    Would it be possible if you could please verify my answer? Thanks if you can help
    Last edited by db5vry; January 16th 2010 at 11:30 PM.
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  2. #2
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    I'm not sure if I've substituted it correctly but all I'm looking for here is to confirm if it's right
    Last edited by db5vry; January 16th 2010 at 11:32 PM.
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