Section 1.4 Complex Numbers

An imaginary number is a number of the form bi where

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 )...
View Full Document

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.

Ask a homework question - tutors are online