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