# Complex Numbers and their Properties

Imaginary numbers as we have discussed in Tuesday’s post are numbers of the form *bi* where is a real number and . The term *imaginary* as (opposed to *real*) was first used by Rene Descartes, the mathematician who invented Coordinate Geometry — the Cartesian plane in particular. Leonhard Euler was the one who introduced the symbol for .

Gerolamo Cardano, a pioneer in probability, was the one who suggested the use of numbers of the form where and are real numbers and . Numbers of this form were named *complex numbers* by Carl Frederich Gauss.The **real part** of is and the **imaginary part** is *bi*.

Note that if we treat these numbers as binomials, then, to add and will result to . Similarly, multiplying gives us

.

The following follow from the operations that we have done above: (1) and (2) Prove this!