Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding - Page 112: 75

The two solutions are complex conjugates.

$3x^{2}-3x+4=0$ To determine the nature of the solutions (without solving), we compute the sign of the discriminant in the quadratic formula ($a=3,\ b=-3,\ c=4$): $b^{2}-4ac=(-3)^{2}-4*3*4=9-48=-39$ Since the discriminant is negative, the two solutions are complex conjugates.