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: Complex Numbers and amplitude

  1. Mar 9, 2010 #1
    Hi this isn't homework, just a practice problem I already have the answer too for my waves class:
    z=sin(wt)+cos(wt)
    Express this in the from Z=Re[Aej(wt+[tex]\alpha[/tex])]

    I know how to express sine in the form of cosine, and cosine in the from of a complex exponential, but I don't know how to do this...I need to find the amplitude and [tex]\alpha[/tex]. Can someone help?
     
  2. jcsd
  3. Mar 9, 2010 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Expand [itex]Re[Ae^{j(\omega t+\alpha)}][/itex] in terms of sin(ωt) and cos(ωt) and compare it to z.
     
  4. Mar 9, 2010 #3
    Well for [itex]Re[Ae^{j(\omega t+\alpha)}][/itex]...the inside equals[itex]Ae^{j(\omega t)}e^{j\alpha}[/tex] and [itex]e^{j\omega t}[/itex]=cos(wt)...I'm not really sure where to go from there.
     
  5. Mar 9, 2010 #4

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You need to get the inside into the form x+iy so you can just pick off the x when you take the real part. Don't break the exponential up. Just use Euler's formula on it.
     
  6. Mar 9, 2010 #5
    Ok so cos(wt)+sin(wt)=Re[Acos(wt+a)]+Re(Ajsin(wt+a)....and now..I don't really get what the Re does, I know that means real, but what is the significance of it here? Am I suppose to take out the j or something?
     
  7. Mar 9, 2010 #6

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You throw away the imaginary part: Re[x+iy]=x.
     
  8. Mar 9, 2010 #7
    Oh I got it thanks!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook