Question

Express the given complex number in the form \(a + ib: i^{-39}\)

Answer 1

\( i^{-39}=i^{-4 × 9-3}\)

\(=(i^{4})^{-9}× i^{-3}\)

\(=\dfrac{1}{i^{-3}}=\dfrac{1}{-i}\)

\(=\dfrac{-1}{i} × \dfrac{i}{i}\)

\(=i\) (Ans.)