Question

Найдите аргумент числа 3i-1/ 2i+1

Answer 1

$\displaystyle z=\frac{3i-1}{2i+1}= \frac{(3i-1)(2i-1)}{(2i+1)(2i-1)} = \frac{-6-3i-2i+1}{-4-1} = \frac{5i+5}{5}=i+1$

Модуль: $|z|= \sqrt{1^2+1^2}= \sqrt{2}$, тогда

       $\displaystyle z=i+1= \sqrt{2} \bigg( \frac{1}{ \sqrt{2} } + \frac{i}{ \sqrt{2} } \bigg)= \sqrt{2} \bigg(\cos \frac{\pi}{4} +i\sin\frac{\pi}{4} \bigg)$

ОТВЕТ: $\varphi=\frac{\pi}{4}$