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Claude ROUXEL: Lecturer at the Conservatoire National des Arts et Métiers
INTRODUCTION
Complex numbers are widely used in electricity. The basic idea behind this set of numbers is to add to the set
of real numbers, a new number,
, 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:
= –1.
= –1.
We then demonstrate that complex numbers can be uniquely written in Cartesian form:
where a and b are real numbers.
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Mathematics for electricians
Cartesian form of complex numbers
