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Real and Complex Roots on Same Plot

How to plot all real and complex roots of the following function in 3-
D using Manipulate by varying constant c?

q = 2.304 ;  z[c_] = q Sin[ c x ] + c Sin[q x]. The real roots of z[c]
= 0 ( 0 < x < 20, 0 < real part of complex root < 20  ) to be plotted
on x-axis, complex conjugates on y-axis, and z[c] on z-axis as c is
varied between  0.5 and 2.0

Thanks  in advance.


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