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plot questions

• To: mathgroup at smc.vnet.net
• Subject: [mg69980] plot questions
• From: dimmechan at yahoo.com
• Date: Thu, 28 Sep 2006 06:17:41 -0400 (EDT)

In connection with a recent post of mine

(http://groups.google.gr/group/comp.soft-sys.math.mathematica/browse_thread/thread/9836d5644ef5b0a1/990d325c2340ea2a?hl=el#990d325c2340ea2a)

I have two questions

The following plots give some insight about the real and
imaginary part of a given function, e.g. cos(x)

ContourPlot[Evaluate[Re[Cos[z] /. z -> x + I*y]], {x, -Pi, Pi}, {y,
-Pi, Pi}, Contours -> 30, PlotPoints -> 30, ContourShading -> None,
Frame -> {True, True, False, False}, FrameLabel -> {"\nRe[z]",
"Im[z]\n"}]

ContourPlot[Evaluate[Im[Cos[z] /. z -> x + I*y]], {x, -Pi, Pi}, {y,
-Pi, Pi}, Contours -> 30, PlotPoints -> 30, ContourShading -> None,
Frame -> {True, True, False, False}, FrameLabel -> {"\nRe[z]",
"Im[z]\n"}]

Is is another way to get a similar plot without using ContourPlot?

Consider now the following function

f[z_] := Cos[z] - z

ref[x_, y_] := Re[f[z] /. z -> x + I*y]
imf[x_, y_] := Im[f[z] /. z -> x + I*y]

Here are two parametric plots

ParametricPlot[{ref[x, y], imf[x, y]} /. y -> Pi, {x, -Pi, Pi}]
ParametricPlot[{ref[x, y], imf[x, y]} /. x -> Pi/3, {y, -Pi, Pi}]

In the previous plot we keep one variable fixed.
What I want (if this is possible) is a plot in which in one axis will
be the real part of f[z] and in the other axis the imaginary but both
x=[z] and y=Im[z] to vary on some range.

Thanks