# Set of Complex Numbers

The set of complex numbers can be defined the set of numbers in the form of , where *i* represents the square root of negative one and *a* and *b* are members of the set of real numbers.

## Definition of a Complex Number

A complex number is an extension of the real number line where in addition to the regular part of the number there is a complex part of the number. The reason why complex numbers are useful is that they allow previously unsolvable problems to be solved. The regular part of the number is denoted by the variable *a* and the complex part is denoted by the variable *b*. The letter *i* represents the square root of negative one.

A complex number can be geometrically interpretted using the complex coordinate plane shown below. Which visualizes the two parts of the number together. The regular part of the number is represented by the horizontal direction and the complex part is represented by the vertical direction.