MATLAB Programming Fundamentals - MathWorks

Calculating the nth Roots of 1

Use the Live Editor to experiment with MATLAB code interactively. Add controls to show

students how important parameters affect the analysis. To add controls, go to the Live

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We can use this last equation to find the nth roots of 1. For example, for any value of n, we

can use the formula above with values of k= 0...n− 1. We can use this MATLAB code to

experiment with different values of n:

n = 6;

roots = zeros(1, n);

for k = 0:n-1

roots(k+1) = cos(2*k*pi/n) + 1i*sin(2*k*pi/n); % Calculate the roots

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 2 π/n.

cla

plot(cos(range),sin(range),'k') % Plot the unit circle

hold on

plot(real(roots),imag(roots),'ro') % Plot the roots

19 Live Scripts and Functions