How can you show two complex functions are 90 degrees out of phase?

[pivoxa15]

Homework Statement

If you are given two complex functions and asked to show that they vary sinusoidally with angular frequency w and 90 degrees out of phase, how would you do that?

The Attempt at a Solution

They vary sinusoidally with angular frequency w if they are of the form
G(z)=e^(iwt)A(z)
H(z)=e^(iwt)B(z)

Would you compute the real and imaginary parts and compare the real parts of each function and the imaginary parts as well. If each differ by 90 degrees than you know the two functions as a whole differ by 90 degrees

 

[berkeman]

Be careful what you mean by z. What is z?

If z is a function of iwt, then there is another iwt term in the A and B functions, which complicates your answer. I think a better form to start with would be something like:

$$G(z) = A e^{(i \omega t + i \theta_g)}$$
$$H(z) = B e^ {(i \omega t + i \theta_h)}$$

Can you tell us why?