Analyze beats using complex exponentials

[Lizwi]

Homework Statement

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

Homework Equations

Ho do I do this problem

The Attempt at a Solution

I changed this into cos and sine terms.

 

[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!

 

[Lizwi]

Thaks, They said: beats occur in sound when two sources emit frequencies that are almost the same. The perceived 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!

 

[tiny-tim]

(try using the X₂ button just above the Reply box )

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.
…
Im done!

noooo, you're not!

read the hint …

they want you to write the answer in terms of p and q, where p = (w₁+w₂)/2 and q = (w₁-w₂)/2

try again ​