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.)