Find the real and imaginary parts $\displaystyle u(x,y), v(x,y)$ of the following functions:
$\displaystyle f(z) = z^3 $
$\displaystyle g(z) = \frac {e^z}{z}$
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