Question

ao dividir 1(-raiz de 3)i por -1+i obtém-se um complexo de argumento igual a ?

Answer 1

$z=\frac{1-i\sqrt{3}}{-1+i}\\\\\frac{1-i\sqrt{3}}{-1+i}.\frac{-1-i}{-1-i}=\frac{-1+i\sqrt{3}-i-\sqrt{3}}{1-i+i-i^2}=\frac{(-1-\sqrt{3})-i+i\sqrt{3}}{2}\\\\|z|=\sqrt{a^2+b^2}\\|z|=\sqrt{\frac{(-1-\sqrt{3}}{2})^2+(\frac{-1+\sqrt{3}}{2})^2}=\sqrt{\frac{1+2\sqrt{3}+3}{4}+\frac{1-2\sqrt{3}+3}{4}}=\sqrt{\frac{8}{4}}=\sqrt{2}\\\\Sen\delta=\frac{b}{|z|}=\frac{\frac{-1+\sqrt{3}}{2}}{\sqrt{2}}=\frac{-1+\sqrt{3}}{2\sqrt{2}}=\frac{-2\sqrt{2}+2\sqrt{6}}{8}=\frac{-\sqrt{2}+\sqrt{6}}{4}$

$Cos\delta=\frac{a}{|z|}=\frac{\frac{-1-\sqrt{3}}{2}}{\sqrt{2}}=\frac{-1-\sqrt{3}}{2\sqrt{2}}=\frac{-2\sqrt{2}-2\sqrt{6}}{8}=\frac{-\sqrt{2}-\sqrt{6}}{4}$