How to draw a geometrical interpretation of Im(z^4)

[x0gt1g2dnoy (michael terry)]

Hi!

Excuse If I made something wrong but I wanted to ask you about a possibility to draw a diagram to show Im of z^4.

How to draw something similar on Wolfram Alpha? I mean the attached picture.

Thank you in advance.

Best wishes.

[bsimpson141421356 (Bill Simpson)]

Perhaps something like

Plot3D[Im[(a + I b)^4], {a, -2, 2}, {b, -2, 2}]

here

[5okgvjduhrj (michael terry)]

Thank you so much.

Is there any way to draw it using just black & white?

[henrikschachner]

Hi Michael,

perhaps this is what you are looking for:

ContourPlot[Im[(a + I b)^4], {a, b} \[Element] Disk[], PlotTheme -> "Monochrome", PlotPoints -> 100, 
   Contours -> #] & /@ {1, 5, 15}

which gives:

Regards – Henrik

[5okgvjduhrj (michael terry)]

Henrik, I’m grateful to you for your help.

The only difference I made was about swapping {a,b} to {b,a}.

Thank you.