Calculate the Cube Roots
To execute individual sections of MATLAB code, go to the Live Editor tab and click the
Run Section button. Output appears together with the code that created it. Create
sections using the Section Break button.
In our case a, b, and c are all equal to 1. The other two roots are calculated from these
formulas:
a = 1 ; b = 1 ; c = 1;
roots = [];
roots(1) = 1;
roots(2) = (-b + sqrt(b^2 - 4ac))/(2a); % Use the quadratic formula
roots(3) = (-b - sqrt(b^2 - 4ac))/(2a);
So the full set of cube roots of 1 are:
disp(roots')
1.0000 + 0.0000i
-0.5000 - 0.8660i
-0.5000 + 0.8660i
Displaying Roots in the Complex Plane
Include plots in the Live Editor so students can visualize important concepts.
We can visualize the roots in the complex plane to see their location.
range = 0:0.01:2*pi;
plot(cos(range),sin(range),'k') % Plot the unit circle
axis square; box off
ax = gca;
ax.XAxisLocation = 'origin';
ax.YAxisLocation = 'origin';
hold on
plot(real(roots), imag(roots), 'ro') % Plot the roots
Create Interactive Course Materials Using the Live Editor