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Modulus of a Complex Number

If z1 and ...

Question

If $z_{1}$ and $z_{2}$ two non-zero 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

- p

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B

p / 2

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C

- p / 2

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D

0

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Solution

The correct option is D $0$
$| z_{1} + z_{2} | = | z_{1} | + | z_{2} |$
$\Rightarrow z_{1} & z_{2}$ are collinear and in same direction.
$\Rightarrow a r g (z_{1}) - a r g (z_{2}) = 0.$
Hence, the answer is $0.$

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