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!