How can i use the roots function to show that all the roots of a complex number lie on a square

Basically i have the polynomial x^4 -16=0, and I want to plot a square showing that the roots of the polynomial represent a square. Thanks!

[James Tursa]

What have you done so far? What specific problems are you having with your code?

Hint: Once you get the four roots, use the real( ) and imag( ) functions to separate the parts and then plot them as the x and y coordinates respectively.

[Pablo Doval]

i got this so far:

>> p = [1 0 0 0 -16];

>> r = roots(p)

r =

-2.0000 + 0.0000i

0.0000 + 2.0000i

0.0000 - 2.0000i

2.0000 + 0.0000i

>> abs(r)

ans =

2.0000

2.0000

2.0000

2.0000

>> plot(real(r),imag(r),'bo')

[Pablo Doval]

when plotting the points on the graph it shows the four points but i want to make a square with the axis in the four points

Answer 1

[James Tursa]

You are really only missing one piece to get the lines plotted. To plot the lines between the points, you first need to order the points so that the connections are along the square edges like you want. A simple way to do this is to sort by phase angle first, then add an extra point to connect the last line. E.g.,

p = [1 0 0 0 -16];
r = roots(p);
[~,a] = sort(angle(r)); % Sort by phase angle
x = real(r); x = x(a); x(end+1) = x(1); % reorder according to sort indexing, add an extra point
y = imag(r); y = y(a); y(end+1) = y(1); % reorder according to sort indexing, add an extra point
plot(x,y,'*-');
axis square
xlim([-3 3]);
ylim([-3 3]);

Answer 2

[Mark Sherstan]

Try this out:

corners = roots([1 0 0 0 -16]);

x = real(corners);
y = imag(corners);

figure(1)
plot(x,y,'*r')
xlim([-4 4])
ylim([-4 4])