# Homework Help: Analyze beats using complex exponentials

1. Mar 1, 2012

### Lizwi

1. The problem statement, all variables and given/known data

Please use the complex algebra to evaluate e^(iω1t)+e^(iω2t), w2 means omega 2?

2. Relevant equations
Ho do I do this problem

3. The attempt at a solution
I changed this into cos and sine terms.

2. Mar 1, 2012

### tiny-tim

ωelcome to PF!

Hi Lizwi! Welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

3. Mar 1, 2012

### Lizwi

Re: Physics question

Thaks, They said: beats occur in sound when two sources emit frequencies that are almost the same. The percieved wave is the sum of the two waves, so that at your ear, the wave is the sum of the two cosines of w1t and w2t........( my w means omega ) use complex algebra two evaluate this. The sum is the real part of e^(w1t)+e^(w2t). notice the two identities w1= (w1+w2)/2 + (w1-w2)/2. Use the complex exponentials to drive the results; dont't just look up some trig identity.

What I did is , because they said the sum is the real part of e^(w1t)+e^(w2t) I wrote this in term of course and sine: (cosw1t + i sinw1t) + (cosw2t + i sinw2t)
(cosw1t + cosw2t) + i (sinw1t + sinw2t)
the real part is cosw1t + cosw2t
Im done!

4. Mar 1, 2012

### tiny-tim

(try using the X2 button just above the Reply box )
noooo, you're not!