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Math Help - complex analysis

  1. #1
    Kai
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    complex analysis

    let z = x + iy and let

    f(z) = 2x(y+1) + i(x^2+2y-y^2)

    find f(z) in terms of z and \bar z

    i only need a start-up

    anybody help?
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  2. #2
    Moo
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    Hello !
    Quote Originally Posted by Kai View Post
    let z = x + iy and let

    f(z) = 2x(y+1) + i(x^2+2y-y^2)

    find f(z) in terms of z and \bar z

    i only need a start-up

    anybody help?
    If z=x+iy, \bar z=x-iy

    Note that z+\bar z=2x and z-\bar z=2iy

    Hence we have :

    \boxed{x=\frac{z+\bar z}{2}} \quad \quad \boxed{y=\frac{z-\bar z}{2i}}

    It may be all you need here


    Edit : notice that if you still have \bar z in the expression of f(z), then the function is not holomorphic =)
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  3. #3
    Kai
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    Quote Originally Posted by Moo View Post
    Hello !

    If z=x+iy, \bar z=x-iy

    Note that z+\bar z=2x and z-\bar z=2iy

    Hence we have :

    \boxed{x=\frac{z+\bar z}{2}} \quad \quad \boxed{y=\frac{z-\bar z}{2i}}

    It may be all you need here


    Edit : notice that if you still have \bar z in the expression of f(z), then the function is not holomorphic =)
    Yep, easy in the end, my mind not working, maybe exam stress
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