1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Simple complex numbers integral

  1. Sep 8, 2008 #1
    1. The problem statement, all variables and given/known data
    Integrate using complex numbers
    \int\limits_0^{2\pi} cos^4(\theta)

    2. Relevant equations
    cos^4(\theta)= (\frac{e^{j\theta} + e^{-j\theta}}2)^4
    3. The attempt at a solution

    \frac 1{2^4} (e^{j\theta} + e^{-j\theta})^4

    I got
    \frac 1{2^4} \int^{2\pi}_0 (e^{4j\theta}+4e^{2j\theta}+4e^{-2j\theta}+e^{-4j\theta}+6)

    After this I am not sure what to do

    The integral of [tex]
    \int e^{4j}[/tex] would be [tex]\frac{e^{4j\theta}}{4j}[/tex]?

    How do I cancel them?

    Input appreciated
  2. jcsd
  3. Sep 8, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Sure, that's the integral of e^(4j*theta). You'll notice if you evaluate it from 0 to 2*pi the result is 0. The same for all the other exponentials. The only term that contributes is the 6.
  4. Sep 8, 2008 #3
    thanks man
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook