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2. Consider the set of nonzero complex numbers, defined by C* = {a+b√-1: a, b = R} - {0}. For example, 2-3√√−1, π + 2√√−1, and 2 + 0√-1 = 2 are elements of C*. Consider the multiplication operation on C* defined by (a+b√−1) (c+d√-1) = ac + ad√−1+ bc√−1+bd (√−1)² = (ac - bd) + (ad + bc) √-1. Show that the inverse of a +b√-1 in C* is equal to a b a² +6² a² +6² √-1. You may assume that the identity element is 1=1+0√-1.

2. Consider the set of nonzero complex numbers, defined by C* = {a+b√-1: a, b = R} - {0}. For example, 2-3√√−1, π + 2√√−1, and 2 + 0√-1 = 2 are elements of C*. Consider the multiplication operation on C* defined by (a+b√−1) (c+d√-1) = ac + ad√−1+ bc√−1+bd (√−1)² = (ac - bd) + (ad + bc) √-1. Show that the inverse of a +b√-1 in C* is equal to a b a² +6² a² +6² √-1. You may assume that the identity element is 1=1+0√-1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. Consider the set of nonzero complex numbers, defined by C* = {a+b√-1: a,b ≤ R} - {0}. For example, 2-3√√−1, π + 2√√−1, and 2 + 0√-1 = 2 are elements of C*. Consider the multiplication operation on C* defined by (a+b√−1) (c+d√−1) = ac + ad√−1 + bc√−1 + bd (v = = (ac - bd) + (ad + bc) √-1. Show that the inverse of a +b√-1 in C* is equal to a b a² +6² a² + b² You may assume that the identity element is 1 = 1 + 0√-1. -1. 2
Transcribed Image Text:2. Consider the set of nonzero complex numbers, defined by C* = {a+b√-1: a,b ≤ R} - {0}. For example, 2-3√√−1, π + 2√√−1, and 2 + 0√-1 = 2 are elements of C*. Consider the multiplication operation on C* defined by (a+b√−1) (c+d√−1) = ac + ad√−1 + bc√−1 + bd (v = = (ac - bd) + (ad + bc) √-1. Show that the inverse of a +b√-1 in C* is equal to a b a² +6² a² + b² You may assume that the identity element is 1 = 1 + 0√-1. -1. 2
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