Question

expresar forma polar de z=3-3i

Answer 1

$<var>\\z=3-3i\\\\ z=|z|(\cos \varphi +i\sin\varphi)\\ |z|=\sqrt{a^2+b^2}\\ |z|=\sqrt{3^2+3^2}\\ |z|=\sqrt{18}\\ |z|=3\sqrt2\\ a>0\Rightarrow\varphi=arctg\ \frac{a}{b}\\ arctg\ \frac{3}{3}=\\ arctg\ 1=\frac{\pi}{4}\\ z=3\sqrt{2}(\cos \frac{\pi}{4} +i\sin\frac{\pi}{4}) </var>$