Question

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

• A. $\frac{5\pi }{12}$
• B. $\frac{\pi }{12}$
• C. $\frac{7\pi }{12}$
• D. $-\frac{\pi }{12}$

Answer 1

Answer: (B)

$\frac{\pi }{12}$

given argument of $z_1,{\overline{z}}_2$ are $\frac{\pi }{3},\frac{\pi }{4}$ respectively

arg($z_1.z_2$)$=arg\left(z_1\right)+arg\left(z_2\right)$

$arg\left(z_2\right)=-arg\left({\overline{z}}_2\right)$

therefore $=\frac{\pi }{3}-\frac{\pi }{4}=\frac{\pi }{12}$