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

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Pablo Doval
Pablo Doval 2018-11-16
编辑： James Tursa 2018-11-16
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!
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Pablo Doval
Pablo Doval 2018-11-16
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
Pablo Doval 2018-11-16
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

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James Tursa
James Tursa 2018-11-16
编辑：James Tursa 2018-11-16
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]);

更多回答（1 个）

Mark Sherstan
Mark Sherstan 2018-11-16
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])
untitled.png

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