end
disp(roots')
1.0000 + 0.0000i
0.5000 - 0.8660i
-0.5000 - 0.8660i
-1.0000 - 0.0000i
-0.5000 + 0.8660i
0.5000 + 0.8660i
Plotting the roots in the complex plane shows that the roots are equally spaced around the unit circle
at intervals of 2π/n.
cla
plot(cos(range),sin(range),'k')
% Plot the unit circle
hold on
plot(real(roots),imag(roots),'ro')
% Plot the roots
Finding the nth roots of -1, i, and -i
Use additional examples to reinforce important concepts. Modify code during the lecture to answer
questions or explore ideas in more depth.
We can find the roots of -1, i, and -i just by using extensions of the approach described above. If we
look at the unit circle we see that the values of 1, i, -1, -i appear at angles 0, π/2, π, and 3π/2
respectively.
Create Interactive Course Materials Using the Live Editor
19-81