Question

Let z be a complex number such that the imaginary part of t is non zero and a = z²+z +1 is real.Then a cannot take the value

• A. $-1$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{3}{4}$

Answer 1

The correct option is D $\frac{3}{4}$

$z^2+z+1-a=0$

$z=\frac{-1\pm \sqrt{4a-3}}{2}$

Here $a\ne \frac{3}{4}$ otherwise $z$ will be purely real.