Question

$z_1$ and $z_2$ be two complex numbers with a and $b$ as their principal arguments, such that $a+b>\pi$, then principal $Arg\left(z_1{z}_2\right)$ is

• A. $\alpha +\beta +\pi$
• B. $\alpha +\beta -\pi$
• C. $\alpha +\beta -2\pi$
• D. $\alpha +\beta$

Answer 1

Answer: (C)

$\alpha +\beta -2\pi$

$arg{z}_1=a$
$arg{z}_2=b$
$a+b>\pi$
$arg\left(z_1{z}_2\right)=arg{z}_1+arg{z}_2=a+b$
Here, $(a+b)$ is one of the arguments but not the principle argument because principle argument E$(-\pi ,\pi )$
$\therefore$ Principle argument $=a+b-2\pi$