Question

If arg($z_1$) = 11 $\frac{\pi }{18}$ and arg ($z_2$) = 19 $\frac{\pi }{18}$, then the principal argument of $z_1$$z_2$ is

• A. (-5 π)/3
• B. (7 π)/3
• C. (-π)/3
• D. None of these

Answer 1

The correct option is C

(-π)/3

arg($z_1$$z_2$) = arg($z_1$) + arg($z_2$) + 2kπ [k=0,1, or -1]

= $\frac{11\pi }{18}$ + $\frac{19\pi }{18}$ + 2kπ

= $\frac{30\pi }{18}$ + 2kπ = $\frac{5\pi }{3}$ + 2kπ

If k = -1,

Arg($z_1$$z_2$) = $\frac{5\pi }{3}$ - 2π

= $\frac{-\pi }{3}$.