one advantage is that it is easy to graph some electrical situations like the magnetic
fields around two conductors carrying current. the complex formula is w=(z-1)/(z+1).
notice the fields are at right angles to each other. REFER TO THE LINK FOR A PICTURE.
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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.
Yes, the complex numbers, as well as the real numbers which are a subset of the complex numbers, form groups under addition.