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It's easy to do. Take the complex number (2+i3). On an x, y plane the 2 would be on the real number line or x=2. 3 would be on the y=3 line where x=2. So you would have a point at (2,3) in the plane.
You can get some interesting graphics from complex plotting programs.
The LINK below shows what the equation w=1/z can do to a photo.
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How complex numbers are used in determining gain of a system?
Since complex numbers can be expressed as magnitude and angle, a plot of a system's response can be approximated with a Bode plot (see related link). The gain is the magnitude, and the phase shift is the angle change of the system.
Why to study complex numbers?
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.
What is the relation of complex numbers to real numbers?
Complex numbers are a proper superset of real numbers. That is to say, real numbers are a proper subset of complex numbers.
Could anyone list numbers not in the set of complex numbers?
No. Complex numbers is the highest set of numbers you can go, and there are no sets outside of complex numbers.
Set of real numbers and set of complex numbers are equivalent?
Real numbers are a proper subset of Complex numbers.
