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Thread: 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

    $\displaystyle w=z^2$

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

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

    u = $\displaystyle x^2 - y^2$
    v = $\displaystyle 2xy$

    Then I inserted the $\displaystyle y=x-1$ into the equations

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

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

    and my cartesian equation came out as

    $\displaystyle v = u + 1$

    Would it be possible if you could please verify my answer? Thanks if you can help
    Last edited by db5vry; Jan 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; Jan 16th 2010 at 11:32 PM.
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