Re: Need help with troublesome complex algebra

From: Robert Israel (israel_at_math.ubc.ca)
Date: 01/07/05 

Date: 7 Jan 2005 03:17:22 GMT

In article <200501062228.j06MSfP23891@proapp.mathforum.org>,
mohammad <matin2018@yahoo.com> wrote:
>i can solve this problem
>tanz=z is real
>ztanz=k k=0,1,2,3

It might help if you actually stated a problem.
I assume you mean "tan(z)" rather than the German word for dance.
tan(z) = z is an equation.
"tan(z)=z is real" is a false statement, because an equation
is not something that can be real.
Do you mean you want to solve the equation tan(z) = z for z, where
z is real?
If so, there are no closed-form solutions other than z=0. You can
use numerical methods such as Newton's to find approximate solutions:
(+/-)4.4934094579090641753, (+/-)7.7252518369377071643,
(+/-)10.904121659428899827, (+/-)14.066193912831473480,
(+/-)17.220755271930768739, (+/-)20.371302959287562845, ...
There's one in each interval ((n-1/2) pi, (n+1/2) pi) for integer n.

Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada