3. The conjugate of the complex number z = a + bi is z= a – bi. Also, |z| = Va² + b². (a) What is the (geometric) relationship between z and z in the complex plane? (b) Consider the equation z² +az+b= 0, with a and b real numbers. Suppose there are two distinct solutions to the equation, and one of them is a non-real number zo. Then show that the other solution is zo. Was that true of the solutions of z2 - 3z + 6 = 0 in Problem 2(a)? (c) Suppose z1 |z1| = |2|. 3 + 4i and z2 = 3 – 4i. Find z1 and z2 in the complex plane, and show that

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 40E
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3. The conjugate of the complex number z = a + bi is z= a – bi. Also, |z| = Va2 + 62.
(a) What is the (geometric) relationship between z and z in the complex plane?
(b) Consider the equation z2+az+b = 0, with a and b real numbers. Suppose there are two distinct
solutions to the equation, and one of them is a non-real number zo. Then show that the other
solution is 7o. Was that true of the solutions of z2 – 3z + 6 = 0 in Problem 2(a)?
3 – 4i. Find z1 and z2 in the complex plane, and show that
(c) Suppose zi =
|21| = |22|.
3 + 4i and z2 =
Transcribed Image Text:3. The conjugate of the complex number z = a + bi is z= a – bi. Also, |z| = Va2 + 62. (a) What is the (geometric) relationship between z and z in the complex plane? (b) Consider the equation z2+az+b = 0, with a and b real numbers. Suppose there are two distinct solutions to the equation, and one of them is a non-real number zo. Then show that the other solution is 7o. Was that true of the solutions of z2 – 3z + 6 = 0 in Problem 2(a)? 3 – 4i. Find z1 and z2 in the complex plane, and show that (c) Suppose zi = |21| = |22|. 3 + 4i and z2 =
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