What is the Complex Analysis and Trig Homework Statement?

[metgt4]

Homework Statement

The principal valueof the logarithmic function of a complex variable is defined to ave its argument in the range -pi < arg(z) < pi. By writing z = tan(w) in terms of exponentials, show that:

tan^-1(z) = (1/2i)ln[(1 + iz)/(1 - iz)]

The Attempt at a Solution

I have absolutely no idea where to start on this problem. My brain must be fried this week, but all I know how to do is write z = tan(w) in terms of exponentials.

z = (1/2i)(e^iw + e^-iw)/(e^iw - e^iw)


Thanks!
Andrew

 

[Dick]

First you'd better check your expansion of z in terms of e^(iw) and e^(-iw). There's more than one mistake in there. Once you done that, put x=e^(iw). Then e^(-iw)=1/x. Solving for z in terms of x just means solving a quadratic equation.