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Homework Help: Complex exponential

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

    write e^z in the form a +bi
    z = 4e^(i*pi/3)

    ---------------------------------------
    My guess:

    z = 4*(cos(pi/3) + i*sin(pi/3))

    e^z = e^(4*(cos(pi/3) + i*sin(pi/3))) = e^(4*cos(pi/3))*(cos(4*sin(pi/3)) + i*sin(4*sin(pi/3)))

    but the solution says

    e^(2)*(cos(2*sqrt(3)) + i*sin(2*sqrt(3)))
     
  2. jcsd
  3. Sep 21, 2010 #2

    gabbagabbahey

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    Homework Helper
    Gold Member

    Well, [itex]\sin(\pi/3)=\frac{\sqrt{3}}{2}[/itex], and I'm sure you know what [itex]\cos(\pi/3)[/itex] is...:wink:
     
  4. Sep 21, 2010 #3
    Thanks for the help.
    --------------------------------------
    z = 4e^(i*pi/3)
    z = 4*(cos(pi/3) + i*sin(pi/3))
    z = 2 + 2*sqrt(3)
    e^z = e^(2)*(cos(2*sqrt(3)) + i*sin(2*sqrt(3))
     
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