Section 1.4 Complex Numbers

# An imaginary number is a number of the form bi where

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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.

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