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How do I find the magnitude of a complex function?

  1. Oct 1, 2011 #1
    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)

    [itex]R(jω) = 1 + \exp{(-jω)} + \exp{(-j2ω)} + \exp{(-j3ω)} + \exp{(-j4ω)}[/itex]

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

    2. Relevant equations

    [itex]R(jω) = 1 + \exp{(-jω)} + \exp{(-j2ω)} + \exp{(-j3ω)} + \exp{(-j4ω)}[/itex]

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

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

    [tex]= |1| + |\exp(-jω)| + |\exp(-j2ω)| + |\exp(-j3ω)| + |\exp(-j4ω)|[/tex]
    [itex]= 1 + 1 + 1 + 1 + 1[/itex]
    [tex]= 5[/tex]

    ?
     
  2. jcsd
  3. Oct 1, 2011 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

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