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Math Help - complex transformtion/mapping

  1. #1
    Junior Member
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    Nov 2009
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    35

    complex transformtion/mapping

    can someone please solve the following problem;

    complex transformtion/mapping-untitled.jpg

    Thanks
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  2. #2
    Newbie
    Joined
    Jan 2010
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    z=x+iy
    w=u+iv

    w=z^2+z-3

    =(x+iy)^2+(x+iy)-3

    =x^2+2ixy-y^2+x+iy-3

    =(x^2-y^2+x-3)+i(2xy+y)

    So:
    u=x^2-y^2+x-3 and v=2xy+y

    (a) If v=c then 2xy+y=c or

    y=\frac{c}{2x+1}

    (b) Re(z)=k so Re(x+iy)=x=k

    So:  u=k^2-y^2+k-3 and v=y(2k+1)

    (c) For c=1: y=\frac{1}{2x+1}

    For k=0: u=-y^2-3 and v=y so u=-v^2-3
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  3. #3
    Junior Member
    Joined
    Nov 2009
    Posts
    35

    Thumbs up

    Quote Originally Posted by Suhada View Post
    z=x+iy
    w=u+iv

    w=z^2+z-3

    =(x+iy)^2+(x+iy)-3

    =x^2+2ixy-y^2+x+iy-3

    =(x^2-y^2+x-3)+i(2xy+y)

    So:
    u=x^2-y^2+x-3 and v=2xy+y

    (a) If v=c then 2xy+y=c or

    y=\frac{c}{2x+1}

    (b) Re(z)=k so Re(x+iy)=x=k

    So:  u=k^2-y^2+k-3 and v=y(2k+1)

    (c) For c=1: y=\frac{1}{2x+1}

    For k=0: u=-y^2-3 and v=y so u=-v^2-3

    Thanks for the help
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