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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- Jan 21st 2010, 01:33 PMCreebeFinding 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 $

$\displaystyle g(z) = \frac {e^z}{z}$ - Jan 21st 2010, 01:47 PMDrexel28
- Jan 21st 2010, 01:56 PMCalculus26
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