Real and Complex Roots presented in a single plot

*To*: mathgroup at smc.vnet.net*Subject*: [mg91820] Real and Complex Roots presented in a single plot*From*: Narasimham <mathma18 at hotmail.com>*Date*: Tue, 9 Sep 2008 06:56:21 -0400 (EDT)

z[x_] = 1.3 Sin[1.7* x] + 0.6 Sin[4* x] ; Plot[z[x], {x, 0, 18}] In the above plot we can see all the real roots of z very approximately at {2.1,3.4, 5.5, 7.6, 9, 11, 13.1, 14.5, 16.5}, as the curve crosses x-axis. We can also recognize and see the real parts of all the complex roots of z where the curve is nearest to x -axis at {1.4, 4.2, 6.6, 9.6, 12.3, 15.3, 17.7}. They are near to x-values where the local maxima/minima occur.But we cannot 'see' their complex parts, as they need to be computed. After computation of all real and complex roots I would like to represent all roots, real and complex roots alike, on an ( x - y ) Argand diagram (in a 2D plot) with the real part on x - axis and imaginary part on y - axis. How to do this ? Regards, Narasimham

**Follow-Ups**:**Re: Real and Complex Roots presented in a single plot***From:*Murray Eisenberg <murray@math.umass.edu>

**Re: Real and Complex Roots presented in a single plot***From:*Daniel Lichtblau <danl@wolfram.com>