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Little confused about raising a complex number to a power.

  1. Jun 12, 2012 #1
    1. The problem statement, all variables and given/known data

    α=2e3∏i/4

    find α11 in cartesian form.


    2. Relevant equations



    3. The attempt at a solution

    It's been a while since I've done these but from what remember you add 2kpi to get exp in the range of -∏,∏.

    so if I let k=15

    I get e3∏i/4

    but the sltn says it needs to be raised to ∏i/4

    can some one please tell me why, should I be adding 4k∏ since it is divided by 4?

    Thanks.
     
  2. jcsd
  3. Jun 12, 2012 #2

    HallsofIvy

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    Oh, dear! I just divided wrong! 33/7= 8+ 1/7.
     
    Last edited: Jun 12, 2012
  4. Jun 12, 2012 #3
    I get something different.. [itex] (e^{3 \pi i /4} )^{11} = e^{33 \pi i /4} = e^{8 \pi i + \pi i/4} = e^{\pi i/4} [/itex]
     
  5. Jun 12, 2012 #4
    Hmm, I get the exponent as [itex]\pi i/4[/itex].

    We have,

    [tex]\vec{p} = e^{3\pi i/4}[/tex]

    Raising the power to 11,

    [tex]\vec{t} = e^{33\pi i/4}[/tex]

    Looking at [itex]33\pi /4[/itex] we see that it crosses the first quadrant[itex](2n\pi)[/itex], 4 times, so that gives an angular displacement of [itex]8\pi[/itex]. Let x be the angle in cartesian range we are looking for,

    [tex]8\pi + x = \frac{33\pi}{4}[/tex]


    Edit : Just saw your edit :tongue2:
     
  6. Jun 12, 2012 #5
    oops I did the same thing, oh damn!

    Thanks for clearing that up anyhow.
     
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