# How do I find the magnitude of a complex function?

1. Oct 1, 2011

### interxavier

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

I'm asked to find the magnitude of a complex function R(jw) = 1 + exp(-jw) + exp(-j2w) + exp(-j3w) + exp(-j4w)

$R(jω) = 1 + \exp{(-jω)} + \exp{(-j2ω)} + \exp{(-j3ω)} + \exp{(-j4ω)}$

where $$ω$$ is the angular frequency $$j$$ is the imaginary number $$j = \sqrt{-1}$$ and $$\exp(-jnw)$$ is a complex sinusoid.

2. Relevant equations

$R(jω) = 1 + \exp{(-jω)} + \exp{(-j2ω)} + \exp{(-j3ω)} + \exp{(-j4ω)}$

3. The attempt at a solution
So what I did was:
$|R(jω)| = |1 + \exp{(-jω)} + \exp{(-j2ω)} + \exp{(-j3ω)} + \exp{(-j4ω)}|$

and I don't know how to proceed from here. Do we have to do it like this:

$$= |1| + |\exp(-jω)| + |\exp(-j2ω)| + |\exp(-j3ω)| + |\exp(-j4ω)|$$
$= 1 + 1 + 1 + 1 + 1$
$$= 5$$

?

2. Oct 1, 2011

### rude man

What is exp(jθ) for any real θ expanded per Euler?
What is |c| given c= a + jb?

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