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Let 21 and 22 be complex numbers. In particular, let z₁ = a + bi and 22 = c + di, where a, b, c, d are real numbers. (a) Show that the conjugate of the sum of 2₁ and 22 is the same as the sum of their conjugates. That is, show that 21+22= 21+%2 (b) Show that the conjugate of the product of 2₁ and 22 is the same as the product of their conjugates. That is, show that 21 22 = 21 22 .

Let 21 and 22 be complex numbers. In particular, let z₁ = a + bi and 22 = c + di, where a, b, c, d are real numbers. (a) Show that the conjugate of the sum of 2₁ and 22 is the same as the sum of their conjugates. That is, show that 21+22= 21+%2 (b) Show that the conjugate of the product of 2₁ and 22 is the same as the product of their conjugates. That is, show that 21 22 = 21 22 .

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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5. Let 2₁ and 22 be complex numbers. In particular, let z₁ = a + bi and 22 = c + di, where a, b, c, d are real numbers. (a) Show that the conjugate of the sum of 2₁ and 22 is the same as the sum of their conjugates. That is, show that 21 +2₂= 2₁ +22 (b) Show that the conjugate of the product of 2₁ and 2₂ is the same as the product of their conjugates. That is, show that 21 22 21 22 Note: It is mathematically poor form to work two sides of an equation at once. You can start on one side and work your way to the other, or work both sides separately and show that your separate calculations give the same result.
Transcribed Image Text:5. Let 2₁ and 22 be complex numbers. In particular, let z₁ = a + bi and 22 = c + di, where a, b, c, d are real numbers. (a) Show that the conjugate of the sum of 2₁ and 22 is the same as the sum of their conjugates. That is, show that 21 +2₂= 2₁ +22 (b) Show that the conjugate of the product of 2₁ and 2₂ is the same as the product of their conjugates. That is, show that 21 22 21 22 Note: It is mathematically poor form to work two sides of an equation at once. You can start on one side and work your way to the other, or work both sides separately and show that your separate calculations give the same result.
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