Question

${\left(\sqrt[3]{3}+\left(3^{5/6}\right)i\right)}^3$ is an integer where $i=\sqrt{-1}$. The absolute value of the integer is equal to

Answer 1

Answer: 24

Solving, ${\left[3^{1/3}(1+\sqrt{3}i)\right]}^3=3(1+\sqrt{3}i{)}^3$
$=3\cdot 8{\left(\cos \frac{\pi }{3}+i\sin \frac{\pi }{3}\right)}^3=-24$