Mathematics - Complex Number Question with Solution | TestHub

$\because \mathrm{Im}(z)\ne 0$ $\Rightarrow z$ is non-real and equation $z^2+z+(1-a)=0$ will have non-real roots, if $D<0$ $\Rightarrow 1-4(1-a)<0$ $\Rightarrow 4a<3\Rightarrow a<\frac{3}{4}$ $\therefore a$ can not take the value $\frac{3}{4}$.