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

Step-by-step solution

Im (z) 0 z is non-real and equation z²+z+(1-a)=0 will have non-real roots, if D < 0 1-4(1-a) < 0 4 a < 3 a < 3 4 a can not take the value 3 4 .