Write the complex number in the form a + bi. square root of six (cos 315° + i sin 315°) (2 points)

[tex]\bf z=\stackrel{r}{6}[cos(\stackrel{\theta }{315^o})+i~sin(\stackrel{\theta }{315^o})]\qquad \begin{cases} a=x=rcos(\theta )\\ b=y=rsin(\theta )\\ ----------\\ a=6cos(315^o)\\ \qquad 6\left( \frac{\sqrt{2}}{2} \right)\\ \qquad 3\sqrt{2}\\ b=6sin(315^o)\\ \qquad 6\left( -\frac{\sqrt{2}}{2} \right)\\ \qquad -3\sqrt{2} \end{cases} \\\\\\ z=(~3\sqrt{2}~,~-3\sqrt{2}~)\implies z=3\sqrt{2}-3\sqrt{2}~i[/tex]