# 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​}]

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Aisha Mohamed on 20 May 2022
Edited: Torsten on 22 May 2022
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

Torsten on 20 May 2022
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)))
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Walter Roberson on 22 May 2022
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);
F = f(X,Y);
surf(X,Y,abs(F), 'edgecolor', 'none')
figure
surf(X, Y, angle(F), 'edgecolor', 'none')
figure
surf(X, Y, angle(F), 'edgecolor', 'none'); view(2)
Torsten on 22 May 2022
Edited: Torsten on 22 May 2022
Thank you, Walter.
r is the radius of the complex number for which you want to evaluate the function.
It can take any non-negative number (except those at which the function has poles).