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I need to find the solution to the equation in the picture, and show graphically that these lie on a circle in the complex number plane. How would one go about this? enter image description here

bittscoterie
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2 Answers2

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and show graphically that these lie on a circle in the complex number plane

You could use the absolute value of one of the solution as the radius

eq = z^5 == -3 + 3*I
sol = z /. Solve[eq, z]  
radius = Abs[sol[[1]]];
p1 = ComplexListPlot[sol, PlotStyle -> Red];
p2 = Graphics[{LightOrange, Disk[{0, 0}, radius]}, Axes -> True];
Show[p2, p1, PlotRange -> All]

Mathematica graphics

Nasser
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3

Or BoundingRegion.

pts = NSolveValues[z^5 == -3 + 3 I, z];
reg = BoundingRegion[ReIm@pts, "MinDisk"];
ComplexListPlot[pts, 
 Prolog -> {EdgeForm[Red], 
   FaceForm[Directive[Opacity[.2], LightBlue]], reg}, 
 PlotRange -> 1.5]

enter image description here

cvgmt
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