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Math Help - Analysis Complex numbers

  1. #1
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    Analysis Complex numbers

    Suppose that f is a function of the complex variable z = x + iy given
    by


    f(x + iy) = (x^3 - axy^2 + 2x^2 - 2by^2 + 1) + i(cyx^2 - y^3 + dxy)
    for some real constants a; b; c; d. It is known that f is entire. What are
    the constants a; b; c; d?
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  2. #2
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    Quote Originally Posted by Richmond View Post
    Suppose that f is a function of the complex variable z = x + iy given
    by


    f(x + iy) = (x^3 - axy^2 + 2x^2 - 2by^2 + 1) + i(cyx^2 - y^3 + dxy)
    for some real constants a; b; c; d. It is known that f is entire. What are
    the constants a; b; c; d?
    I would suggest that you look at the "Cauchy-Riemann" equations that must be satified at every z.
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