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Complex exponentials - homework

  1. Feb 12, 2017 #1
    • Thread moved from the technical Math forums, so no Homework Template is shown
    Could you give me a hint how to attack this problem?

    Find a complex number z = a+i*b such that f(t)=Re e^(z*t) where f(t)=cos(2*pi*t)

    I have begun as follows:

    e^((a+i*b)*t)=e^(a*t)*(cos(b)+i*sin(b))

    Re e^(z*t)= e^(a*t)*cos(b)

    What to do now?
     
  2. jcsd
  3. Feb 12, 2017 #2

    Ssnow

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    Hi, ##t## is real? If is yes so you must find ##a,b## from ##e^{at}\cos{b}=cos(2\pi t)## ...
     
  4. Feb 12, 2017 #3
    Yes, t is a real variable.I know I must but how? Thank you very much. :)
     
  5. Feb 12, 2017 #4

    Ssnow

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    Gold Member

    another hint: ## e^{at}cos{(b)}=e^{0t}cos{(2\pi t)}##, you can read now ##a=...## and ##b=...##
     
  6. Feb 12, 2017 #5
    Ok, I got it. :) Great. Thank you very much. :)
     
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