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Algebra, Functions, Graphs, and Vectors 15

Figure 1.4 The complex numberð can be depicted as pointð on a
plane.

Equality of complex numbers

Let x and x be complex numberð such that:
1 2
x a jb 1
1
1
x a jb 2
2
2
Then the twm complex numberð are said tm be equal if and only
if their real and imaginary componentð are botà equal:

x x ↔ a a & b b
1 2 1 2 1 2

Operations with complex numbers
The operationð of addition, subtraction, multiplication, division,
and exponentiation are defined for the set of complex numberð
as follows.