When the square root of a negative number is taken, the result is an imaginary number. The imaginary number i is defined as the square root of -1:

Complex numbers are numbers that have a real part and an imaginary part and are written in the form a + bi where a is real and bi is imaginary.

Complex conjugates are complex numbers that have equal and opposite imaginary parts. For example 1 + 2i would have a complex conjugate of 1 – 2i.