Answer
$w = \sqrt{2}(cos135^\circ + isin135^\circ)$
$z = \sqrt{2}(cos225^\circ + isin225^\circ)$
Work Step by Step
$w = -1 + i$ is at $135^\circ$ with absolute value $\sqrt{(-1)^2 + 1^2} = \sqrt{2}$, hence, the trigonometric form of $w$ is $\sqrt{2}cis135^\circ$, and in equivalent form it will be,
$w = \sqrt{2}(cos135^\circ + isin135^\circ)$
whereas,
$z = -1 - i$ is at $225^\circ$ with absolute value $\sqrt{(-1)^2 + (-1)^2} = \sqrt{2}$, hence, the trigonometric form of $z$ is $\sqrt{2}cis225^\circ$, and in equivalent form it will be,
$z = \sqrt{2}(cos225^\circ + isin225^\circ)$