# Math Help - Finding the Real/Imaginary Part of f(z), g(z)

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

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

$f(z) = z^3$
$g(z) = \frac {e^z}{z}$

2. Originally Posted by Creebe
Find the real and imaginary parts $u(x,y), v(x,y)$ of the following functions:

$f(z) = z^3$
$g(z) = \frac {e^z}{z}$
What is this? Is this partial derivatives?

3. 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