What does this mean? Help with imaginary number problem!

To have real coeeficients there has to be a    -  i    root also

Quadratic formula:

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)      

     shows that to have an i root the discriminant has to be NEGATIVE...and the disriminant is a + or - term....so there will be ANOTHER -2i root to go with the +2 i root

To expand on EP's answer

If   a + bi    is a root of a polynomial......then so is  a - bi

These are known as "conjugate pairs"  

Thus....if we have complex roots of a polynomial, they will occur in pairs

So   the conjugate of  0 + 2i    is    0 - 2i