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Consider the quadratic equation 22 – 4z + 8 = 0. a) Show that the complex solutions of the quadratic equation are z = 2+ 2i and z = 2 – 2i. b) Convert z= 2+ 2i to polar form, and hence use De Moivre's theorem to find 2 in polar form and Cartesian form. c) Find the three cube roots of z = 2+ 2i in polar form and Cartesian form.

Consider the quadratic equation 22 – 4z + 8 = 0. a) Show that the complex solutions of the quadratic equation are z = 2+ 2i and z = 2 – 2i. b) Convert z= 2+ 2i to polar form, and hence use De Moivre's theorem to find 2 in polar form and Cartesian form. c) Find the three cube roots of z = 2+ 2i in polar form and Cartesian form.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.4: Complex And Rational Zeros Of Polynomials
Problem 36E
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Consider the quadratic equation 22 – 4z + 8 = 0. a) Show that the complex solutions of the quadratic equation are z = 2+ 2i and z = 2 – 2i. b) Convert z= 2+ 2i to polar form, and hence use De Moivre's theorem to find 2 in polar form and Cartesian form. c) Find the three cube roots of z = 2+ 2i in polar form and Cartesian form.
Transcribed Image Text:Consider the quadratic equation 22 – 4z + 8 = 0. a) Show that the complex solutions of the quadratic equation are z = 2+ 2i and z = 2 – 2i. b) Convert z= 2+ 2i to polar form, and hence use De Moivre's theorem to find 2 in polar form and Cartesian form. c) Find the three cube roots of z = 2+ 2i in polar form and Cartesian form.
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