For all complex numbers z satisfying Im(z)≠0, if f(z)=z^2+z+1 is a real valued function, then find its range.
(a) (-∞, -1]
(b) (-∞, 1/3)
(c) (-∞, 1/2]
(d) (-∞, 3/4)
I had been asked this question in an interview for job.
My enquiry is from Functions of a Complex Variable topic in portion Complex Function Theory of Engineering Mathematics