Extend polynomial identities to complex numbers for higher-degree polynomial work.
Solve a polynomial over the complex numbers by factoring and using conjugate complex factors
Problem
Solve \(x^{4}~-~16~=~0\) over the complex numbers.
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What this problem is really about
Over the complex numbers, factoring is complete only when every nonconstant factor is linear. Use a familiar polynomial identity to break the higher-degree expression into quadratics, then split both differences and sums of squares. The zero-product property turns those linear factors into roots, and the total root count should agree with the original degree.
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