ELEMENTARY MATHEMATICS
W W L CHEN and X T DUONG
c
W W L Chen, X T Duong and Macquarie University, 1999.
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Chapter 9
COMPLEX NUMBERS
9.1.
Introduction
It is easy to see that the equation
x
2
+ 1 = 0 has no solution
x
∈
R
. In order to “solve” this equation,
we have to introduce extra numbers into our number system.
Define the number i by writing i
2
+ 1 = 0. We then extend the collection of all real numbers
by adjoining the number i, which is then combined with the real numbers by the operations addition
and multiplication in accordance with the rules of arithmetic for real numbers. The numbers
a
+
b
i,
where
a, b
∈
R
, of the extended collection are then added and multiplied in accordance with the rules
of arithmetic for real numbers, suitably extended, and the restriction i
2
+ 1 = 0. Note that the number
a
+ 0i, where
a
∈
R
, behaves like the real number
a
.
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 Spring '10
 Goh
 Math, Complex Numbers, Complex number, W W L Chen, T DUONG

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