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​}]

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

Answer 1

[Torsten]

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)))

[Aisha Mohamed]

Hi Torsten

Thank you very much for your help

As I understood you used polar coordonate to plot the absolute value of this function , I have two questions please

1- areyou chose r as arbitrary variable that can take any value

2- I used this code

surf(x,y,angle(f(X,Y)),'edgecolor','none')

to plot the phase of this function but it did not work, how can i write the phase of this function?

Thanks

[Walter Roberson]

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]

@Walter Roberson

Thank you, Walter.

@Aisha Mohamed

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).