what is the reason for having imaginary numbers in math and what are they?

Answer 1

The imaginary unit, i, is defined as the square root of negative one. That is, i = sqrt(-1). Any number that is the product of i and a real number is called an imaginary number. Any number that is the sum of an imaginary number and a real number is called a complex number. Complex numbers are in some ways analagous to cartesian points. The number 2 + 3i can be equated to the ordered pair (2, 3). Complex numbers have many applications in fields such as electronics (where impedance in complex circuits can be modeled as a complex number) and higher-level matrix algebra.

Answer 2

e^(j*w)=cos(w)+j sin(w)
euler's equation.
imaginary numbers are just a way to represent cosine and sine functions because they are on a circle so it imaginary numbers tell 'how much' and 'what direction'. Electrical Engineers shift into that domain all the time, because it's so much easier to work with the sines and cosine functions, and all the many rules to work with it. It's way easy to work in the imaginary domain.

Don't be fooled by the word imaginary though, it's not a good term. Touch an imaginary voltage, and you'll know that it is not imaginary at all.

Answer 3

it's a bad name. imaginary does not equal fake in this case. they have physical interpretations in some problems that are too advanced for me.