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Thread: Finding the Real/Imaginary Part of f(z), g(z)

  1. #1
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    Finding the Real/Imaginary Part of f(z), g(z)

    Find the real and imaginary parts $\displaystyle u(x,y), v(x,y)$ of the following functions:

    $\displaystyle f(z) = z^3 $
    $\displaystyle g(z) = \frac {e^z}{z}$
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Creebe View Post
    Find the real and imaginary parts $\displaystyle u(x,y), v(x,y)$ of the following functions:

    $\displaystyle f(z) = z^3 $
    $\displaystyle g(z) = \frac {e^z}{z}$
    What is this? Is this partial derivatives?
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  3. #3
    MHF Contributor Calculus26's Avatar
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    For #2

    z= x + iy

    e^z = e^(x+iy) = e^x e^(iy) = e^x[cos(y)+isin(y)]

    e^z/z = e^x[cos(y)+isin(y)]/(x + iy)

    multiply top and bottom by x - iy and collect real and imaginary parts

    For # 1 I think you're just going to have to multiply out (x+iy)^3

    using (a+b)^3 = a^3 +3a^2b + 3ab^2 + b^3
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