Expresar forma polar de z = 3 - 3i?

<img src="https://tex.z-dn.net/?f=%5C%5Cz%3D3-3i%5C%5C%5C%5C%20z%3D%7Cz%7C%28%5Ccos%20%5Cvarphi%20%2Bi%5Csin%5Cvarphi%29%5C%5C%20%7Cz%7C%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D%5C%5C%20%7Cz%7C%3D%5Csqrt%7B3%5E2%2B3%5E2%7D%5C%5C%20%7Cz%7C%3D%5Csqrt%7B18%7D%5C%5C%20%7Cz%7C%3D3%5Csqrt2%5C%5C%20a%3E0%5CRightarrow%5Cvarphi%3Darctg%5C%20%5Cfrac%7Ba%7D%7Bb%7D%5C%5C%20arctg%5C%20%5Cfrac%7B3%7D%7B3%7D%3D%5C%5C%20arctg%5C%201%3D%5Cfrac%7B%5Cpi%7D%7B4%7D%5C%5C%20z%3D3%5Csqrt%7B2%7D%28%5Ccos%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20%2Bi%5Csin%5Cfrac%7B%5Cpi%7D%7B4%7D%29%20" />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}) " alt = " \ \ 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}) " align = "absmiddle" class = "latex - formula">.