There are many reasons, but the one I'm fond of is that if you plot a complex equation, you can visualize certain aspects of say electricity. A plot of w=(z-1)/(z+1)
can show a possible electromagnetic field of two wires carrying current as depicted
in the below LINK.
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Yes. But until you study complex numbers, there is no solution.
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.
1. A complex formula like (z+1/z) is used to study and design airplane wings. 2. I use complex numbers to make math related art. The LINK below shows artwork based on the formula (z-1)/(z+i)