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Real and Complex Roots presented in a single plot

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 ?


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