Question

Let $z_1$ and $z_2$ be two non-zero complex numbers such that $|z_1|+|z_2|=|z_1+z_2|$. STATEMENT-1 : amp $\left(z_1\right)$ = amp $\left(z_2\right)$
and
STATEMENT-2 : In complex plane $z_1,z_2$ and the origin must be collinear.

• A. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
• B. Statement-1 is False, Statement-2 is True
• C. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
• D. Statement-1 is True, Statement-2 is False

Answer 1

The correct option is A Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

$|z_1|+|z_2|=|z_1+z_2|$ implies $z_1,z_2$ are origin are collinear with $z_1$ and $z_2$ on the same side of $O$.

Both Statement-1 and Statement-2 are true but Statement-2 doesn’t fully explain Statement-1. Hence answer is (2).