MATLAB and Complex Numbers Examples
To start you may type
Format rat
i =sqrt(-1)
Matlab will return
ans =
To enter a complex number type
c1= 4+5i
To find the conjugate of c1 type
conj(c1)
You may ask for the real part of a complex number by typing
real(c1)
Imaginary part of the number can be obtained by typing
imag(c1)
To enter a complex matrix, enter it in the same way that you enter a real matrix:
A= [ 2+i 3-5i, -2; -7i 6+7i 55-12i]
This is what you will see
A = 2 + 1i 3 - 5i -2
0 - 7i 6 + 7i 55 - 12i
You may find the real part, imaginary part or the conjugate of a matrix by typing the following commands:
real(A)
imag(A)
conj(A)
To find the conjugate transpose of a matrix use the following command
A'
The commands det(A), rref(A), roots(p) , poly(A), eig(A) work in the same way that they work for real matrices. Note that A' will provide the conjugate transpose of A.
Examples:
Type
B=[2+3i 3-i 5-7i; 9+i 5+i 2-i; 2-i 3-4i 4+i]
To find determinant of B type
det(B)
To find the conjugate transpose of B type
B'
To find coefficients of the characteristic polynomial of B type
poly(B)
To find reduced row echelon form of B type
rref(B)
to find the inverse of B type
inv(B)
to find eigenvalues of B type
eig(B)
to find eigenvalues and eigenvectors of B type
[V D] = eig(B)
