Question

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

Answer 1

$\Rightarrow (-1+\sqrt{3}i{)}^3$
$\Rightarrow -1+3\sqrt{3}i-3(-3)-3\sqrt{3}i$ $[\because (a-b{)}^3=a^3-b^3-3ab(a-b)]$

$\Rightarrow -1+9=8$

It is a real number.