Complex numbers are numbers of the a + bi where a and b are real number and i is the imaginary square root of -1.
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The answer will depend on the form of the fourth root. Positive real numbers will have two fourth roots which are real and two that are complex. Complex numbers will have four complex roots. However, none of these can be "simplified" in the normal sense of the term.
Complex numbers are a proper superset of real numbers. That is to say, real numbers are a proper subset of complex numbers.
No. Complex numbers is the highest set of numbers you can go, and there are no sets outside of complex numbers.
Real numbers are a proper subset of Complex numbers.
Complex numbers include real numbers, pure imaginary numbers, and the combination of those two.