They were discovered when Cardano solved the third degree equation.
In the formulas that arose to solve the third degree equation, Cardano needed to take the square root of negative numbers and add them up in a certain way. The strange thing that happened was that the formulas used these complex numbers, even if the solutions to the equation where all real. This baffled the mathematicians of the time, because how could these strange numbers turn out to be "real"?
Later this was considered totally correct, when the field of complex numbers was better undestood.
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Complex math covers how to do operations on complex numbers. Complex numbers include real numbers, imaginary numbers, and the combination of real+imaginary numbers.
The complex numbers are a field.
All of them. Real numbers are a subset of complex numbers.
Gerolamo Cardano is an Italian mathematician who introduced complex numbers. Complex numbers are those that can be expressed in the form of a+bi where a and b represent real numbers.
Yes, all real numbers are complex numbers.