$\sqrt{-1}$ is a real number.

Q. $1+\sqrt{3}$ is a real rational number.

Q. The real value of $\theta$ for which the expression $\frac{1+i\cos \theta }{1-2i\cos \theta }$ is a real number is:

Q. Show that $(-1+\sqrt{3}i{)}^3$ is a real number.

Q. If $w$ is a non-real complex number such that $\frac{w-\overline{w}z}{1-z}$ is a real number, then the set of values of $z$ is

Q. Show that $1+i^{10}+i^{20}+i^{30}$ is a real number