0\; ,\; \; tg\varphi =-\frac{\sqrt2/2}{\sqrt2/2}=-1\; \Rightarrow \\\\\varphi\in (\frac{\pi}{2},\pi )\\\\arctg(-1)=-arctg1=-\frac{\pi}{4}\in (-\frac{\pi}{2},0)\\\\argz=\varphi =\pi -arctg1=\pi -\frac{\pi}{4}=\frac{3\pi }{4}\in (\frac{\pi}{2},\pi )" alt="z=-3+3i\\\\|z|=\sqrt{(-3)^2+3^2}=\sqrt{18}=3\sqrt2\\\\cos\varphi =\frac{-3}{3\sqrt2}=-\frac{\sqrt2}{2}<0\; \; ,\; \; sin\varphi =\frac{3}{3\sqrt2}=\frac{\sqrt2}{2}>0\; ,\; \; tg\varphi =-\frac{\sqrt2/2}{\sqrt2/2}=-1\; \Rightarrow \\\\\varphi\in (\frac{\pi}{2},\pi )\\\\arctg(-1)=-arctg1=-\frac{\pi}{4}\in (-\frac{\pi}{2},0)\\\\argz=\varphi =\pi -arctg1=\pi -\frac{\pi}{4}=\frac{3\pi }{4}\in (\frac{\pi}{2},\pi )" align="absmiddle" class="latex-formula">