Mathematics for electricians - Complex numbers

Complex numbers are widely used in electricity. The basic idea behind this set of numbers is to add to the set $ℝ$ of real numbers, a new number, $\text{j}$ , whose square is (–1).

This new set of numbers is designed to :

• retain the operating rules for the reals (associativity, commutativity, distributivity, etc.) ;

• take into account the new rule: ${\text{j}}^2$ = –1.

We then demonstrate that complex numbers can be uniquely written in Cartesian form: $\underset{\_}{z}=a+\text{j}b$

where a and b are real numbers.