Answer
$w\cdot z$
= $2$
Work Step by Step
For $w$, the trigonometric form of it is $\sqrt{2}cis135^\circ$
whereas,
for $z$, the trigonometric form of it is $\sqrt{2}cis225^\circ$
The product of $w$ and $z$ will be
$w\cdot z$
= $\sqrt{2}cis135^\circ\cdot$ $\sqrt{2}cis225^\circ$
= $(\sqrt{2})^2 cis(135^\circ + 225^\circ)$ (Product Theorem)
= $2 cis360^\circ$
= $2 (1 + 0i)$
= $2$