Fundamentals of Technical Mathematics

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 (i=−1).

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,

x=Rez(realpartofz),y=Imz(imaginarypartofz)

For example, the following are complex numbers:

0+0i=