Question

Express the given complex number in the form$a + ib: (-2-\dfrac{1}{3}i)^3$

Answer 1

$(-2-\dfrac{1}{3}i)^3$

$=-[2^3+(\dfrac{i}{3})^3+3.(2)(\dfrac{i}{3})(2)(2+\dfrac{i}{3})]$

$=-[8+\dfrac{i^3}{27}+2i(2+\dfrac{i}{3})]$

$=-[8-\dfrac{i}{27}+4i-\dfrac{2}{3}]$

$=-[\dfrac{22}{7}+\dfrac{107}{27}i]$

$=-\dfrac{22}{3}-\dfrac{107}{27}i$ (Ans.)