complex identities

**hurz** · April 9th 2011, 05:25 PM

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!

**dwsmith** · April 9th 2011, 05:38 PM

Originally Posted by hurz

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

**hurz** · April 9th 2011, 05:52 PM

Originally Posted by dwsmith

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!

**dwsmith** · April 9th 2011, 06:01 PM

Originally Posted by hurz

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.

**dwsmith** · April 9th 2011, 06:04 PM

Originally Posted by hurz

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.

**hurz** · April 9th 2011, 06:19 PM

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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