Complex numbers are those numbers that can be separated into both a real component and an imaginary component. Complex numbers are generally expressed in the form a + bi, where a represents any real number (rational or irrational) and b represents the real coefficient (rational or irrational) of the imaginary number bi. The symbol i represents the square root of -1. Since a + 0i = a, the set of all complex numbers wholly contains the set of purely real numbers. Similarly, since 0 + bi = bi, the set of complex numbers wholly contains the set of purely imaginary numbers. Complex numbers, then, can be considered linear combinations of real and imaginary numbers.

The set of complex numbers is closed under both addition and multiplication, making it a as well as a vector space. Addition and with complex numbers are similar to addition and subtraction with real numbers, with the sums...