how do you find the roots with zero real part of a complex matrix in matlab

To find the roots with zero real part of a complex matrix in MATLAB, you can use the eig function to calculate the eigenvalues of the matrix, and then filter out the eigenvalues with zero real part. Here's an example code snippet:

main.m
% Define your complex matrix
A = [1+2i, 2+1i; 3+1i, 5-2i];

% Calculate the eigenvalues
eigenvalues = eig(A);

% Select eigenvalues with zero real part
zero_real_part_roots = eigenvalues(abs(real(eigenvalues)) < 1e-10);

disp(zero_real_part_roots);
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In this code snippet, A is your complex matrix for which you want to find the roots with zero real part. We calculate the eigenvalues using eig(A) and then filter out the eigenvalues with zero real part using abs(real(eigenvalues)) < 1e-10. Finally, we display the roots with zero real part.

Remember to adjust the threshold 1e-10 based on the precision you need for your specific problem.