# Thread: Complex Analysis: Trig Functions

1. ## Complex Analysis: Trig Functions

Find all solutions to:
1) $cosh(z)=-1$-----done
2) $cos^2 (z)=4$
3) $tan(z)=i$

2. Remember that

$\cos(z)=\frac{e^{iz}+e^{-iz}}{2}$

This gives

$\left(\frac{e^{iz}+e^{-iz}}{2} \right)^2=4 \iff e^{2iz}+2+e^{-2iz}=16$

$(e^{2iz})^2-14e^{2iz}+1=0$

This is quadratic in $e^{2iz}$

Can you finish from here?

You will use a similar trick for tangent just write it as exponentials.

3. I finished from there.

Thanks.

I got (3) to be no solution.