Question

What are the characteristics of a complex number?

Answer 1

complex numbers are numbers that have both a real and non real part, using variables, a + bi, where i is the standard unit for an imaginary number, and a and b are real numbers

Answer 2

the idea originated from the question of taking square roots of negative numbers. If you get your calculator out and try and do
\[\sqrt{-4}\]
it won't like you.
So mathematicians make the definition
\[\sqrt{-1} = i\]
so one can answer problems like the above
\[\sqrt{-4} = \sqrt{-1}\sqrt{4} = 2i\]