\(\displaystyle{r}^{{2}}={\left({x}^{{2}}+{y}^{{2}}\right)}{\left({\left(-{1}\right)}^{{2}}+{1}^{{2}}\right)}={2}\)

\(\displaystyle{r}=\sqrt{{2}}\ {u}{n}{i}{t}{s}\)

\(\displaystyle\theta={{\tan}^{{-{1}}}\cdot}\frac{{y}}{{x}}={{\tan}^{{-{1}}}{\left(-{1}\right)}}=-\frac{\pi}{{4}}\)

Hence, the polar coordinates are \(\displaystyle{\left(\sqrt{{2}},-\frac{\pi}{{4}}\right)}\)