From: rusin@vesuvius.math.niu.edu (Dave Rusin)
Newsgroups: sci.math
Subject: Re: Help on complex trigo
Date: 24 Nov 1996 06:22:28 GMT

In article <57236o$arc@avdat1.bgu.ac.il>, eliz <eliz@bgumail.bgu.ac.il> wrote:

>How do I use complex numbers on trigrometric function, such as tg(z)?

Once you've decided you're interested in complex arguments anyway, you may
as well abandon the trigonometric functions altogether, since
cos(z) = (exp(zi)+(exp(-zi))/2 and sin(z) = (exp(zi)-exp(-zi))/(2i). By taking
reciprocals and quotients you can express the other four standard
trig functions in terms of the exponential function as well.

Of course you can then reverse this if you prefer. That is, 
exp(a+bi)= exp(a)*(cos(b) + i sin(b)) and so (assuming you know how to
perform the arithmetic operations with complex numbers) you can express
any trig function  at complex arguments using rational combinations of
values of  exp  cos  and  sin  .

dave