# Imaginary Unit and Standard Complex Form

## Imaginary Unit and Standard Complex Form

The Imaginary Unit is defined as
i =√-1

The reason for the name “imaginary” numbers is that when these numbers were first proposed several hundred years ago, people could not “imagine” such a number.

It is said that the term “imaginary” was coined by René Descartes in the seventeenth century and was meant to be a derogatory reference since, obviously, such numbers did not exist. Today, we find the imaginary unit being used in mathematics and science. Electrical engineers use the imaginary unit (which they represent as j ) in the study of electricity.

Imaginary numbers occur when a quadratic equation has no roots in the set of real numbers.

A pure imaginary number can be written in bi form where  b  is a real number and   i   is   √-1

A complex number is any number that can be written in the  standard form  a  +  bi,  where a  and  b are real numbers and  i  is the imaginary unit. .

A complex number is a real number a, or a pure imaginary number bi, or the sum of both.

Note these examples of complex numbers written in standard a + bi form: 2 + 3i, -5 + bi .