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Unformatted text preview: ry number is a number of the form bi where b is a
real number.
Note that i = √ −1. We call i the principle square root of −1. x2 In general, if
= −b for some real number b , then
√
√
x = ± bi and we call bi the principle square root of −b .
Example
5i and √ 2i are imaginary numbers. √
The principal square root of −12 is 2 3i .
√
−36 = 6i . Outline Imaginary Numbers Complex Numbers The Arithmetic of the Complex Numbers The Set of Complex Numbers
Deﬁnition
The set of complex numbers is the set
C = {a + bi  a, b ∈ R}.
We call a + bi the standard form of a complex number.
Example 2 √
4 + 3 −20
Write
in standard form. Identify a and b .
2
Write 7 in standard form. Identify a and b . 3 Write −2i in standard form. Identify a and b . 1 Note: N ⊆ W ⊆ Z ⊆ Q ⊆ R ⊆ C. Outline Imaginary Numbers Complex Numbers The Arithmetic of the Complex Numbers Adding and Subtracting Complex Numbers
Adding complex numbers:
(a + bi ) + (c + di ) = (a + c ) + (b + d )i .
Subtracting complex numbers:
(a + bi )...
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This note was uploaded on 02/10/2014 for the course MATH 1050 taught by Professor K.jplatt during the Spring '14 term at Snow College.
 Spring '14
 K.JPlatt
 Algebra, Imaginary Numbers, Complex Numbers

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