How to calculate and plot this function f(z) =\frac{1}{2}[\frac{(z^3)-(0.5+0.8660i)}{z^4-(0.5-0.8660i)z^3}]

Question

Aisha Mohamed 2022-5-20

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1723900-how-to-calculate-and-plot-this-function-f-z-frac-1-2-frac-z-3-0-5-0-8660i-z-4-0-5-0-86

编辑： Torsten 2022-5-22

How can I simplify and plot this function:

$ f(z) =\frac{1}{2}[\frac{(z^3)-(0.5+0.8660i)}{z^4-(0.5-0.8660i)z^3}] $

I am trying to calculate and plot this function but because it is fraction function I thought to multib it in the conjogate of the denomater but I always find the variable z in the numerator and denomurator this did not enable me to simplyfy this function also I can not plot it.

can anybody help me to do that?

Thanks

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Answer 1

Torsten 2022-5-20

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1723900-how-to-calculate-and-plot-this-function-f-z-frac-1-2-frac-z-3-0-5-0-8660i-z-4-0-5-0-86#answer_968380

在 MATLAB Online 中打开

f = @(x,y) 0.5./(x+1i*y).^3.*((x+1i*y).^3-exp(1i*pi/3))./((x+1i*y)-exp(-1i*pi/3));
r = 0.2:0.01:0.9;
phi = 0:0.01:2*pi;
[R,PHI] = meshgrid(r,phi);
X = R.*cos(PHI);
Y = R.*sin(PHI);
surf(X,Y,abs(f(X,Y)))