3.3. Complex numbers
Complex numbers are used in engineering, science, and other technology applications, especially, in control engineering.
Definition of complex number
A complex number is a number that can be written in standard form as
a +
bi, where
a and
b are real numbers and
i is an imaginary unit

.
We call a the real part of the complex number and bi the imaginary part of the complex number. The imaginary unit (number) i is sometimes denoted by j.
For a complex number, z has the rectangular form as z = x + yi, where x and y are real numbers,
For example, the following are complex numbers: