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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.

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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.

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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 ...

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