# Complex conjugate

1. Jan 16, 2013

### JPBenowitz

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

So we are given $\alpha$exp(i$\varpi$t) +$\alpha$*exp(-i$\varpi$t) and are asked to prove the resulting equation is real.

2. Relevant equations

$\alpha$ + $\alpha$* = 2Re($\alpha$) and Euler's Identity

3. The attempt at a solution

I tried expanding out the exp's to cosines and isines but couldn't reach the solution.

2. Jan 16, 2013

### Mute

What if you also write $\alpha = a + i b$, where a and b are both real numbers? Can you do the problem then?

3. Jan 16, 2013

### JPBenowitz

I figured it out but I didn't do it that way. That seems awfully more tedious than usual.

4. Jan 16, 2013

### Mute

It's more tedious than the quick solution, yes, but it was more along the lines of the approach you had tried to take by expanding the exponentials into sines and cosines, so I opted to guide you along that direction, in case the problem wanted you to show it explicitly.

5. Jan 16, 2013

### Dick

Why are you writing a bar over the omega? If omega is real then it's sort of obviously true. Because you are adding two complex conjugates. If omega isn't real then it's not even true.

Last edited: Jan 16, 2013