1. Not finding help here? Sign up for a free 30min 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!

Simple complex numbers integral

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


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

    \frac 1{2^4} (e^{j\theta} + e^{-j\theta})^4
    [/tex]

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

    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

    Dick

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Simple complex numbers integral
  1. Simple complex number (Replies: 3)

Loading...