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Math Help - quick question on complex no.s...I just need a start..

  1. #1
    KAS
    KAS is offline
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    quick question on complex no.s...I just need a start..

    hey there..
    I have an assignment to submit early morning tomorrow..and I really want 2 get an idea about this problem..
    it's on complex no.s
    Evaluate:
    (cosα +isinα)^4 / (sinα + icosα)^5

    for the icos α part I want to ask.. what's the possible way to solve it?
    Like shall I subtract the angle α from 90 degrees? ('pi over 2') or...?
    I'd really appretiate ur help... just so I can start the question atleast..
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  2. #2
    MHF Contributor red_dog's Avatar
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    For (\cos\alpha+i\sin\alpha)^4 use the Moivre formula (\cos\alpha+i\sin\alpha)^n=\cos n\alpha+i\sin n\alpha

    For (\sin\alpha+i\cos\alpha)^5 use the formula \sin\alpha=\cos\left(\frac{\pi}{2}-\alpha\right) and \cos\alpha=\sin\left(\frac{\pi}{2}-\alpha\right) then the Moivre formula.

    Then use \displaystyle\frac{\cos\alpha+i\sin\alpha}{\cos\be  ta+i\sin\beta}=\cos(\alpha-\beta)+i\sin(\alpha-\beta)
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