How do I find the magnitude of a complex function?

[interxavier]

Homework Statement

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.

Homework Equations

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

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:

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

?

 

[rude man]

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