Question

Let z be a complex number such that the imaginary part of z is nonzero and a = z2 + z + 1 is real. Then a cannot take the value (A) –1 (B) 1 3 (C) 1 2 (D) 3 4
A. -1
B. `(1)/(3)`
C. `(1)/(2)`
D. `(3)/(4)`

Answer 1

Correct Answer - D
Given equations is `z^(2) + z + 1 - a = 0`
Cleary this equation do not have real roots if `D lt 0`
` rArr 1- 4 (1-a) lt 0`
` rArr 4a lt 3`
`a lt (3)/(4)`