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    Finding cube roots (a problem in complex analysis)

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    Find all cube roots of the number -8 and state the final answer in rectangular coordinates.

    © BrainMass Inc. brainmass.com March 4, 2021, 7:27 pm ad1c9bdddf

    Solution Preview

    To find the roots of a complex number, we can use the formula

    c = r^(1/3) exp[i(theta/n + 2k(pi)/n)], k=0,1,2,...,n-1

    So, let's apply this to our particular problem.

    We have n=3, k=0,1,2. So,

    =8^(1/3) exp[i(theta/3 + 2k(pi)/3)], k=0,1,2. Theta is equal to the angle measure ...

    Solution Summary

    A step-by-step solution is provided. The student is shown how to find all (complex) cube roots of a number. Word file included.