Question

Let $z_1$ and $z_2$ be two complex numbers with $\alpha$ and $\beta$ as their principal arguments such that $\alpha +\beta >\pi ,$then principal arg $\left(z_1{z}_2\right)$ is given by

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

Answer 1

The correct option is B $\alpha +\beta -\pi$

Principle are $\left(z_1{z}_2\right)$

$=\alpha +\beta \pm n\pi$

$=\alpha +\beta -\pi$