Definition of a Complex Number
The standard equation for complex numbers is:
$ a + bj = c $
The $ a $ in the equation is the real part, and the $ bj $ in the equation is the imaginary part.
Some examples are listed below.
Examples
$ j = \sqrt-1 $
$ j^2 = -1 $
$ j^3 = -j $
$ j^4 = 1 $
$ 8 + 3j + 12 - j = 20 + 2j $
$ 3j (4 - 6j) = 18 + 12j $
$ (-2 + 4j) (1 - 2j) = -2 + 8j + 8 = 6 + 8j $
Source
Signals & Systems 2nd Edition Authors: S. Hamid Nawab, Alan V. Oppenheim, Alan S. Willsky
