Use the discriminant and select whether the roots of 4x 2 - 3x + 3 = 0 are real or imaginary.

To find the discriminant we use b^2 - 4ac

equation of 4x^2 - 3x + 3 = 0

a b c

-3^2 - 4 (4) (3) = - 39

if b^2 - 4ac < 0, there are 2 complex roots or ... no real roots ... in this case imaginary.