Question

If $\frac{\pi }{3}$ and $\frac{\pi }{4}$ are the arguments of $z_1$ and $\overline{z_2}$, then the value of $\arg \left(z_1{z}_2\right)$ is

• A. $\frac{5\pi }{12}$
• B. $\frac{\pi }{12}$
• C. $-\frac{5\pi }{12}$
• D. $-\frac{\pi }{12}$

Answer 1

The correct option is B $\frac{\pi }{12}$

$\arg \left(z_1{z}_2\right)=\arg \left(z_1\right)+\arg \left(z_2\right)$
$\Rightarrow \arg \left(z_1{z}_2\right)=\frac{\pi }{3}-\frac{\pi }{4}=\frac{\pi }{12}$