Question

If $arg\left(z\right)<0$, then $arg(-z)-arg\left(z\right)$ equals

• A. $\pi$
• B. $-\pi$
• C. $-\frac{\pi }{2}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is A $\pi$

$arg\left(\frac{z_1}{z_2}\right)=arg\left(z_1\right)-arg\left(z_2\right)\therefore arg(-z)-arg\left(z\right)=arg\left(\frac{-z}{z}\right)=arg(-1)=\pi$