# Homework Help: Complex notation

1. Sep 21, 2010

### w3390

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

If x= Acos($$\omega$$t + $$\delta$$), then one can also write it as x = Re(B$$e^{i\Phi}$$). Find B and $$\Phi$$ in terms of A, $$\omega$$, and $$\delta$$ if B is real.

2. Relevant equations

3. The attempt at a solution

Not sure where to start on this one. I know you guys can't give answers. All I'm looking for is where to get started. Any help would be appreciated.

2. Sep 21, 2010

### Staff: Mentor

Are you familiar with converting between the rectangular and polar forms of complex numbers? See partway down this wiki page:

http://en.wikipedia.org/wiki/Polar_coordinate_system

.

3. Sep 21, 2010

### w3390

Actually, I think I might have something.

Euler's formula says: e^(i*phi) = cos(phi) + i*sin(phi)

The real part of this is: Re(e^(i*phi)) = cos(phi).

Therefore, the real part of Be^(i*phi) is: Bcos(phi).

So I have: X = Bcos(phi) and X = Acos(wt + delta)

Am I able to just compare the two equations to get the following relationships:

B = A

PHI = wt + delta

It can't be that simple, can it?

4. Sep 21, 2010