Complex fourier series question

[wo83]

Homework Statement

What is the fundamental period of f(x) = e^ax+ibx where a, b are real numbers greater than zero? Find the Fourier series for f(x).

Homework Equations

The Attempt at a Solution

I am able to find the Fourier series for trig based functions but am not sure how to start this one. I was wondering if someone could give me a hint as to how to go about tackling it. My guess would be I have to simplify the function using euler's formula and then go about finding the series in the normal way.

Any hints anyone could offer on this would be greatly appreciated. Thanks

 

[wo83]

nobody have any ideas?

 

[LCKurtz]

You might use the complex form of the FS. For a function of period 2p:

$$f(x) = \sum_{-\infty}^{\infty} c_n e^{\frac{in\pi x}{p}}$$

where

$$c_n = \frac 1 {2p}\int_{-p}^p f(x) e^{-\frac{i n \pi x}{p}}\, dx$$