Question

What is the conjugate & amplitude of $\frac{2i-1}{5}$

Answer 1

Let $z=\frac{2i-1}{5}$.

Now conjugate of $z=\overline{z}=\frac{-2i-1}{5}$.

As $(\frac{2}{5},-\frac{1}{5})$ lies in the fourth quadrant, the amplitude of $z$ is $-{\tan }^{-1}\left|\frac{-1/5}{2/5}\right|=-{\tan }^{-1}\frac{1}{2}$.