Adding two complex functions?

[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.

[tiny-tim]

Hi kasse! :smile:

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

[kasse]

Danke schön

[HallsofIvy]

Hi kasse! :smile:

Hint: eiA + B = eiA + eiB, so divide by the first half of the righthand side, and use eiC + e-iC = 2cosC. :wink:
Oh, dear, oh, dear, oh, dear, tiny-tim! eiA + B = (eiA)(eiB).

[tiny-tim]

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

Geman for oops! :redface:

[kasse]

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