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Math Help - complex no. problem no.1

  1. #1
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    complex no. problem no.1

    question: suppose that
    E = (\frac{1+\sqrt 3 i}2)^n+(\frac{-1+\sqrt 3 i}2)^n
    where n is a natural no.
    find the value of E for
    a) n = 3k
    b) n = 3k +1
    c) n = 3k + 2
    where k is an odd no.

    sorry that i don't type my malfunction workings.
    thanks!
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi

    You should try using the exponential form of the two complex numbers : it'll make the manipulation of the powers easier.
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  3. #3
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    Quote Originally Posted by flyingsquirrel View Post
    Hi

    You should try using the exponential form of the two complex numbers : it'll make the manipulation of the powers easier.
    thanks but i haven't learn exponential yet!
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  4. #4
    Super Member flyingsquirrel's Avatar
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    OK. You may know De Moivre's formula instead ?

    \left(\cos x+\imath \sin x\right)^n=\cos (nx)+\imath \sin (nx)
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  5. #5
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    Use the following with the above post.
    \frac{1}{2} + i\frac{{\sqrt 3 }}{2} = \cos \left( {\frac{\pi }{3}} \right) + i\sin \left( {\frac{\pi }{3}} \right)\,\& \,\frac{{ - 1}}{2} + i\frac{{\sqrt 3 }}{2} = \cos \left( {\frac{{2\pi }}{3}} \right) + i\sin \left( {\frac{{3\pi }}{3}} \right)<br />
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