The Italian mathematician, Gerolamo Cardano conceived of complex numbers around 1545.
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To do calculations using complex numbers.
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.