1. ## complex identities

Hello. Im having trouble to prove this coplex identities, using the exponencial forms:
1)$\displaystyle \tan(z1+z2) = \frac {\tan(z1)+tan(z2)} {1- \tan(z1)* \tan(z2)}$
2)$\displaystyle \tan(\frac{z}{2})=\frac{\sin(z)}{1+\cos(z)}$
where z is a complex number x+iy
Thanks!

2. Originally Posted by hurz
Hello. Im having trouble to prove this coplex identities:
1)$\displaystyle \tan(z1+z2) = \frac {\tan(z1)+tan(z2)} {1- \tan(z1)* \tan(z2)}$
2)$\displaystyle \tan(\frac{z}{2})=\frac{\sin(z)}{1+\cos(z)}$
where z is a complex number x+iy
Thanks!
Write tan(z) as sine over cosine

3. 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!

4. Originally Posted by hurz
Hello. Im having trouble to prove this coplex identities:
1)$\displaystyle \tan(z1+z2) = \frac {\tan(z1)+tan(z2)} {1- \tan(z1)* \tan(z2)}$
2)$\displaystyle \tan(\frac{z}{2})=\frac{\sin(z)}{1+\cos(z)}$
where z is a complex number x+iy
Thanks!
Number one is a basic Trig identity. Look up Sum and Difference Formula.

5. Originally Posted by hurz
Hello. Im having trouble to prove this coplex identities:
1)$\displaystyle \tan(z1+z2) = \frac {\tan(z1)+tan(z2)} {1- \tan(z1)* \tan(z2)}$
2)$\displaystyle \tan(\frac{z}{2})=\frac{\sin(z)}{1+\cos(z)}$
where z is a complex number x+iy
Thanks!

For 2, let $\displaystyle w=\frac{z}{2}$ and use double angle formulas.

6. 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.