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Math Help - help me in complex numbers

  1. #1
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    help me in complex numbers

    Using De’Moivre’s Theorem, prove that

    cos^4 θ= 1/8 cos4θ + 1/2 cos2θ+ 3/8

    Kindly show the solution,

    Thanks.
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  2. #2
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    Quote Originally Posted by Salman91 View Post
    Using De’Moivre’s Theorem, prove that

    cos^4 θ= 1/8 cos4θ + 1/2 cos2θ+ 3/8

    Kindly show the solution,

    Thanks.
    Show us what you have done, then we will explain any errors

    CB
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  3. #3
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    i don't know thats why i have come here, so please help me
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  4. #4
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    Quote Originally Posted by Salman91 View Post
    i don't know thats why i have come here, so please help me
    Start with:

    \displaystyle (\cos (\theta)+i \sin(\theta))^4= \cos(4\theta)+i\sin(4\theta)

    Expand the left hand side and equate real parts on both sides of the resulting equation. Now it should be just an exercise in the repeated application of trig identities.

    CB
    Last edited by CaptainBlack; July 8th 2010 at 04:23 AM.
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  5. #5
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    Quote Originally Posted by CaptainBlack View Post
    Start with:

    \displaystyle (\cos (\theta)+i \sin(\theta))^4= \cos(4\theta)+i\sin(\theta)

    Expand the left hand side and equate real parts on both sides of the resulting equation. Now it should be just an exercise in the repeated application of trig identities.

    CB
    Actually it's

    (\cos{\theta} + i\sin{\theta})^4 = \cos{(4\theta)} + i\sin{(4\theta)}.
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