Given, \((x, y) = (4, −4)\) For the polar coordinates \(r = \sqrt{x^2 + y^2}\ and\ \theta = tan^−1 (\frac{y}{x})\)

\(r = \sqrt{16 + 16}\)

\(r = \sqrt{32}\)

\(r = 4 \sqrt 2\) And \(\theta = tan^-1 (\frac{-4}{4}\)

\(\theta = tan^-1 (-1)\)

\(\theta = \frac{\pi}{4}\) The two sets of polar coordinates are \((-4 \sqrt2, \frac{\pi}{4}). (4 \sqrt2, \frac{\pi}{4})\)