Finding the real component of a two dimensional wave

1. Oct 4, 2014

rmjmu507

1. The problem statement, all variables and given/known data
Show that if the displacement of the waves on a membrane of width b is given by the superposition

$z=A_1\exp^{i(\omega t-(k_1x+k_2y))}+A_2\exp^{i(\omega t-(k_1x-k_2y))}$

with $z=0$ when $y=0$ and $y=b$ then the real part of z is

$z=2A_1sin(k_2)sin(\omega t-k_1x)$ where $k_2=\frac{n\pi}{b}$

2. Relevant equations

3. The attempt at a solution

So I've found that $A_1=-A_2$ and $k_2=\frac{n\pi}{b}$, but I don't quite see how I can show that the real part of z is $z=2A_1sin(k_2)sin(\omega t-k_1x)$. Can someone please provide some guidance?

2. Oct 5, 2014

BvU

How do you find the real part of a complex $z$ ?