Complex numbers are the square roots of negative numbers. i.e. root -1 = i
they use numbers not words.
electrical engineers and quantum mechanics use them.
Yes, many
You can use computers or other digital equipment. OR You can use numbers and do arithmetic.
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.
computers, calculators
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
when you multiply it with another polynomial
Complex numbers can help visualize physical effects like the electromagnetic fields around wires carrying current. Refer to the link below.
Yes. Integers, Real Numbers, and even Complex Numbers can as well.