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One use is to compact a large area into a small one or vice versa. The complex

formula is 1/z, which is inversion. All pairs of complex numbers with absolute value less than 1 will be transformed outside the unit circle and the infinite complex plane will be compacted inside the unit circle! This simple formula produces the real part u=x/(xx+yy) and imaginary part v=-y/(xx+yy). Points approaching infinity will go to zero inside the unit circle!

Q: Why use complex numbers?

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electrical engineers and quantum mechanics use them.

Yes, many

I'm not sure about how to use complex numbers to do this, but I've posted a link to a pretty neat website about Synthetic Division.

using contraction and expansion

Complex numbers are a proper superset of real numbers. That is to say, real numbers are a proper subset of complex numbers.

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Complex numbers are the square roots of negative numbers. i.e. root -1 = i

yes it does

electrical engineers and quantum mechanics use them.

Yes, many

I suggest you read the Wikipedia article con complex numbers, specifically the section "Applications". One example is electrical engineering: in the case of AC, it helps to express all voltages, currents and impedances (equivalent of resistances) as complex numbers.

Complex math covers how to do operations on complex numbers. Complex numbers include real numbers, imaginary numbers, and the combination of real+imaginary numbers.

I'm not sure about how to use complex numbers to do this, but I've posted a link to a pretty neat website about Synthetic Division.

when you multiply it with another polynomial

using contraction and expansion

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.

Complex numbers can help visualize physical effects like the electromagnetic fields around wires carrying current. Refer to the link below.