1. Nov 16, 2008

kasse

How can I show that

$$Aexpi(\omega t - kx + \phi_{1}) + Aexpi(\omega t + kx + \phi_{2}) = 2Aexpi(\omega t + \frac{\phi_{1} + \phi_{2}}{2})cos(kx - \frac{\phi_{1} - \phi_{2}}{2})$$? My book states this without proof, as if it was obvious.

2. Nov 16, 2008

tiny-tim

Hi kasse!

Hint: eiA + B = eiA + eiB, so divide by the first half of the righthand side, and use eiC + e-iC = 2cosC.

3. Nov 16, 2008

kasse

Danke schön

4. Nov 16, 2008

HallsofIvy

Staff Emeritus
Oh, dear, oh, dear, oh, dear, tiny-tim! eiA + B = (eiA)(eiB).

5. Nov 16, 2008

tiny-tim

oops!

Geman for oops!

6. Nov 16, 2008

kasse

eiA + B = (eiA)(eB)....?