\(\displaystyle{\left({4},-\frac{\pi}{{4}}\right)}\)

\(\displaystyle\therefore{r}={4},\theta=-\frac{\pi}{{4}}\)

\(\displaystyle\therefore{x}={r}{\cos{\theta}}={4}{\cos{{\left(-\frac{\pi}{{4}}\right)}}}={4}\cdot\frac{\sqrt{{2}}}{{2}}={2}\sqrt{{2}}\)

\(\displaystyle{y}={r}{\sin{\theta}}={4}{\sin{{\left(-\frac{\pi}{{4}}\right)}}}={4}\cdot{\left(-\frac{\sqrt{{2}}}{{2}}\right)}=-{2}\sqrt{{2}}\)

\(\therefore\)The cartesian/rectangle coordinate

\(\displaystyle{\left({x},{y}\right)}={\left({2}\sqrt{{2}},-{2}\sqrt{{2}}\right)}\)