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Distance between Parallel Lines

If z1 and ...

Question

If $z_{1}$ and $z_{2}$ are two nonzero complex number such that $| z_{1} | + | z_{2} | = | z_{1} + z_{2} |$ then $a r g z_{1} - a r g z_{2}$ is equal to

A

- π

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B

\frac{π}{2}

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C

- \frac{π}{2}

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D

0

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Solution

The correct option is D $0$
$| z_{1} | + | z_{2} | = | z_{1} + z_{2} |$ can only occur when $z_{1}$ is parallel to $z_{2}$ on argand diagram.
Therefore
$a r g (z_{1}) - a r g (z_{2})$ will be $0$
Hence, option 'D' is correct..

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