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Vector Addition

If z1, z2...

Question

If $z_{1}$ , $z_{2}$ are two complex number such that $| z_{1} | = | z_{2} |$ and arg $z_{1} +$ arg $z_{2} = 0$ then $z_{1}$ , $z_{2}$ and

A

Equal

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B

Not equal

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C

Conjugate to each other

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D

Need not be conjugate

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Solution

The correct option is C Conjugate to each other
$| z_{1} | = | z_{2} |$
Also, $a r g (z_{1}) = - a r g (z_{2})$
Hence, $z_{1}$ & $z_{2}$ lie on opposite side of real axis with same modulus
Hence, $| z_{1} | = | z_{2} |$ &
$a r g (z_{1}) = θ = - a r g (z_{2}) = - (- θ)$
$∴ z_{1}$ & $z_{2}$ are conjugates of each other

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