MATLAB Programming Fundamentals - MathWorks

Complex Numbers

Creating Complex Numbers

Complex numbers consist of two separate parts: a real part and an imaginary part. The

basic imaginary unit is equal to the square root of -1. This is represented in MATLAB by

either of two letters: i or j.

The following statement shows one way of creating a complex value in MATLAB. The

variable x is assigned a complex number with a real part of 2 and an imaginary part of 3 :

x = 2 + 3i;

Another way to create a complex number is using the complex function. This function

combines two numeric inputs into a complex output, making the first input real and the

second imaginary:

x = rand(3) * 5;

y = rand(3) * -8;

z = complex(x, y)

z =

4.7842 -1.0921i 0.8648 -1.5931i 1.2616 -2.2753i

2.6130 -0.0941i 4.8987 -2.3898i 4.3787 -3.7538i

4.4007 -7.1512i 1.3572 -5.2915i 3.6865 -0.5182i

You can separate a complex number into its real and imaginary parts using the real and

imag functions:

zr = real(z)

zr =

4.7842 0.8648 1.2616

2.6130 4.8987 4.3787

4.4007 1.3572 3.6865

zi = imag(z)

zi =

-1.0921 -1.5931 -2.2753

-0.0941 -2.3898 -3.7538

-7.1512 -5.2915 -0.5182

Complex Numbers