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Math Help - complex number

  1. #1
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    complex number

    If x, y, a and b are real numbers and if x+yi=a/(b+cosA+icosA) , show that (b2-1)(x2+y2) +a2 = 2abx. (i= imaginary number)

    I got a feeling that it may have something to do with the formula z+1/z = 2cosx and z-1/z =2isinx. But I just can't figure it out.
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  2. #2
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    Re: complex number

    Typo?

    x+yi=a/(b+cosA+icosA)

    should be

    x+yi=a/(b+cosA+isinA)
    Thanks from topsquark
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  3. #3
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    Re: complex number

    Quote Originally Posted by Idea View Post
    Typo?

    x+yi=a/(b+cosA+icosA)

    should be

    x+yi=a/(b+cosA+isinA)
    yeah, you are right, typing mistake^^
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  4. #4
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    Re: complex number

    b+\cos  A+i \sin  A = \frac{a}{z}

    \cos  A+i \sin  A = \frac{a}{z}-b
    Thanks from topsquark
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  5. #5
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    Re: complex number

    Quote Originally Posted by Idea View Post
    b+\cos  A+i \sin  A = \frac{a}{z}

    \cos  A+i \sin  A = \frac{a}{z}-b
    so should I convert cosA to (1/2)(z+1/z) and isinA to (1/2)(z-1/z) ????
    Can you explain more?
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  6. #6
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    Re: complex number

    what is A?
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  7. #7
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    Re: complex number

    I assume A is an arbitrary value (angle) and since it does not appear in the final answer, we should try to eliminate A

    using

    \cos ^2A+\sin ^2A=1
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  8. #8
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    Re: complex number

    Quote Originally Posted by Idea View Post
    I assume A is an arbitrary value (angle) and since it does not appear in the final answer, we should try to eliminate A

    using

    \cos ^2A+\sin ^2A=1
    I understand that. But I could'nt get cos^2 A +sin^2 A without multiplying (cosA-isinA) to the other side, right?
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  9. #9
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    Re: complex number

    The magnitude of a complex number w=a+i b is defined as

    |w|=\sqrt{a^2+b^2}
    Thanks from Trefoil2727
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