Mathematics, 17.04.2020 01:23 NathanaelLopez
For each odd positive integer n, the only real number solution to LaTeX: x^n=1x n = 1 is LaTeX: x=1x = 1 while for even positive integers n, LaTeX: x=1x = 1 and LaTeX: x=-1x = − 1 are solutions to LaTeX: x^n=1x n = 1. In this problem we look for all complex number solutions to LaTeX: x^n=1x n = 1 for some small values of n.
1. Find all complex numbers a + bi whose cube is 1.
2.Find all complex numbers a + bi whose fourth power is 1.
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For each odd positive integer n, the only real number solution to LaTeX: x^n=1x n = 1 is LaTeX: x=1x...
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