3
$\begingroup$

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

New contributor
Bryan is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
$\endgroup$
0

2 Answers 2

3
$\begingroup$

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

$\endgroup$
3
$\begingroup$

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

$\endgroup$

Your Answer

Bryan is a new contributor. Be nice, and check out our Code of Conduct.

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.