Question

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

Answer 1

$(\dfrac{1}{3}+3i)^3$

$=(\dfrac{1}{3})^3+(3i)^{3}+3(\dfrac{1}{3}(3i)(\dfrac{1}{3}+3i))$

$=\dfrac{1}{27}-27i+i+9i^2$

$=\dfrac{1}{27}-27i+i-9$

$=\dfrac{-242}{27}-26i$ (Ans.)