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Math Help - complex identities

  1. #1
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    complex identities

    Hello. I`m having trouble to prove this coplex identities, using the exponencial forms:
    1) \tan(z1+z2) = \frac {\tan(z1)+tan(z2)} {1- \tan(z1)* \tan(z2)}
    2) \tan(\frac{z}{2})=\frac{\sin(z)}{1+\cos(z)}
    where z is a complex number x+iy
    Thanks!
    Last edited by hurz; April 10th 2011 at 03:22 AM.
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  2. #2
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    Quote Originally Posted by hurz View Post
    Hello. I`m having trouble to prove this coplex identities:
    1) \tan(z1+z2) = \frac {\tan(z1)+tan(z2)} {1- \tan(z1)* \tan(z2)}
    2) \tan(\frac{z}{2})=\frac{\sin(z)}{1+\cos(z)}
    where z is a complex number x+iy
    Thanks!
    Write tan(z) as sine over cosine
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  3. #3
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    Quote Originally Posted by dwsmith View Post
    Write tan(z) as sine over cosine
    I did it already. See, i've done a lot of identities proofs, and i had trouble just in these 2. I already did the standard stuff.
    Thank's!
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  4. #4
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    Quote Originally Posted by hurz View Post
    Hello. I`m having trouble to prove this coplex identities:
    1) \tan(z1+z2) = \frac {\tan(z1)+tan(z2)} {1- \tan(z1)* \tan(z2)}
    2) \tan(\frac{z}{2})=\frac{\sin(z)}{1+\cos(z)}
    where z is a complex number x+iy
    Thanks!
    Number one is a basic Trig identity. Look up Sum and Difference Formula.
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  5. #5
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    Quote Originally Posted by hurz View Post
    Hello. I`m having trouble to prove this coplex identities:
    1) \tan(z1+z2) = \frac {\tan(z1)+tan(z2)} {1- \tan(z1)* \tan(z2)}
    2) \tan(\frac{z}{2})=\frac{\sin(z)}{1+\cos(z)}
    where z is a complex number x+iy
    Thanks!

    For 2, let w=\frac{z}{2} and use double angle formulas.
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  6. #6
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    I thought that, but the intention of these question is to use exponencial forms to prove them, not to import trigonometric identities to real numbers.
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