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

${\rm{\alpha }} + {\rm{\beta }} - {\rm{\pi }}$

${\rm{\alpha }} + {\rm{\beta }} + {\rm{\pi }}$

${\rm{\alpha }} + {\rm{\beta }} + 2{\rm{\pi }}$

${\rm{\alpha }} + {\rm{\beta }}$

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Understanding +4 | -1

Let

{z_1}

and

{z_2}

be two complex numbers with

\alpha

and

\beta

as their principle arguments such that

\mathrm{\alpha } + \mathrm{\beta } > \mathrm{\pi },

then principal

\arg \left( {{z_1}{z_2}} \right)\;

is given by

View answer and explanation

Correct option: B

\mathrm{\alpha } + \mathrm{\beta } - \mathrm{\pi }

Option B (

\alpha + \beta - \pi

) is correct because the principal argument must lie between

-\pi

and

\pi

, and since

\alpha + \beta > \pi

, we subtract

2\pi

to bring it into the range.