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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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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