real and imaginary parts of tan(z)

**Roxanne123456789** · December 13th 2009, 02:46 PM

Hi, firstly i am confused as to what tan(z) is. Is it just tan(x+iy) and how do i find the real and imaginary parts of it? From this how do i find the solutions to tan(z) = 0?
Thanks.

**tonio** · December 13th 2009, 06:23 PM

Originally Posted by Roxanne123456789

Hi, firstly i am confused as to what tan(z) is. Is it just tan(x+iy) and how do i find the real and imaginary parts of it? From this how do i find the solutions to tan(z) = 0?
Thanks.

$\tan z=\frac{\sin z}{\cos z}\,,\,\sin z=\frac{e^x-e^{-z}}{2i}\,,\,\cos z=\frac{e^z+e^{-z}}{2}$

Now do some algebra (for example, multiplying the whole thing by $\frac{e^z}{e^z}$ and...

Tonio

**Roxanne123456789** · December 17th 2009, 05:58 AM

Could i not just use sin(z)=sin(x+iy) so Re(sin(z))= sin(x)cosh(y) and Im(sin(z)) = cos(x)sinh(y) and do the same for cos(x+iy) and then find the real and imaginary parts of tan(z) that way?

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