The polar form of $ z $ is:
$$ z = 20 \sqrt{ 2 } \cdot \left ( cos ~ 315^o + i \cdot sin ~ 315^o \right) $$The polar form of the complex number $ z = a + bi$ is:
$$ z = r \cdot \left(cos~\theta + i \cdot sin ~ \theta \right) $$where, $ r $ is the modulus of $ z $ and $~ \theta ~$ is an argument of $ z $.
The moduo for $ a = 20 $ and $ b = -20 $ is:
$$ r = \sqrt{a^2 + b^2} = \cdots =20 \sqrt{ 2 } $$To find argument $ \theta $ we use one of the following formulas:
$$ \begin{aligned} \theta & = \arctan \left( \frac{b}{a} \right) \text{ if } a > 0 \\ \theta & = \arctan \left( \frac{b}{a} \right) + 180^o \text{ if } a < 0 \\ \\ \theta & = 90^o \text{ if } a = 0 \text{ and } b > 0 \\ \\ \theta & = 270^o \text{ if } a = 0 \text{ and } b < 0 \end{aligned} $$In this example: $ a = 20 $ and $ b = -20 $ so:
$$ \theta = arctan \left( \frac{b}{a} \right) $$$$ \theta = arctan \left( \frac{ -20 }{ 20 } \right) $$$$ \theta = arctan \left( -1 \right) $$$$ \theta = 315^o $$