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Complex notation

  1. Sep 21, 2010 #1
    1. The problem statement, all variables and given/known data

    If x= Acos([tex]\omega[/tex]t + [tex]\delta[/tex]), then one can also write it as x = Re(B[tex]e^{i\Phi}[/tex]). Find B and [tex]\Phi[/tex] in terms of A, [tex]\omega[/tex], and [tex]\delta[/tex] if B is real.

    2. Relevant equations



    3. The attempt at a solution

    Not sure where to start on this one. I know you guys can't give answers. All I'm looking for is where to get started. Any help would be appreciated.
     
  2. jcsd
  3. Sep 21, 2010 #2

    berkeman

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    Staff: Mentor

    Are you familiar with converting between the rectangular and polar forms of complex numbers? See partway down this wiki page:

    http://en.wikipedia.org/wiki/Polar_coordinate_system

    .
     
  4. Sep 21, 2010 #3
    Actually, I think I might have something.

    Euler's formula says: e^(i*phi) = cos(phi) + i*sin(phi)

    The real part of this is: Re(e^(i*phi)) = cos(phi).

    Therefore, the real part of Be^(i*phi) is: Bcos(phi).

    So I have: X = Bcos(phi) and X = Acos(wt + delta)

    Am I able to just compare the two equations to get the following relationships:

    B = A

    PHI = wt + delta


    It can't be that simple, can it?
     
  5. Sep 21, 2010 #4

    berkeman

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    Staff: Mentor

    :biggrin:
     
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