Let w be a given complex number. In this problem, we aim to outline the procedure for finding all solutions z to the equation z3=w(a) First of all, notice that z=1 is one solution to the equation z3=1. Find the other 2 solutions. Enter each of your response in the form a+bi, and separate your answers by semicolons. (b) Compute (1+3 i)3. Enter your response in the form a+bi. (c) Let w be the complex number you obtained from (b), and consider the equation z3=w. Notice that your work from (b) shows that z=1+3 i is one of the solutions to this equation. Now find the other 2 solutions. Enter each of your response in the form a+bi, and separate your answers by semicolons.

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Answered: separate your answers by semicolons.…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.3: Quadratic Equations

Problem 81E

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Let w be a given complex number. In this problem, we aim to outline the procedure for finding all solutions z to the equation z³=w

(a) First of all, notice that z=1 is one solution to the equation z³=1. Find the other 2 solutions. Enter each of your response in the form a+bi, and separate your answers by semicolons.

(b) Compute (1+3 i)³. Enter your response in the form ‌a+bi‌.

(c) Let w be the complex number you obtained from (b), and consider the equation z³=w. Notice that your work from (b) shows that z=1+3 i is one of the solutions to this equation. Now find the other 2 solutions. Enter each of your response in the form ‌a+bi, and separate your answers by semicolons.

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