Engineering (especially electrical engineering), Math, Physics mainly.
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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.
Complex numbers can help visualize physical effects like the electromagnetic fields around wires carrying current. Refer to the link below.
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.