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Let z(1),z(2) be two complex numbers suc...

Let `z_(1),z_(2)` be two complex numbers such that `|z_(1)+z_(2)|=|z_(1)|+|z_(2)|`. Then,

A

arg`(z_(1))="arg"(z_(2))`

B

`"arg"(z_(1))+"arg"(z_(2))=pi/2`

C

`|z_(1)|=|z_(2)|`

D

`z_(1)z_(2)=1`

Text Solution

Verified by Experts

The correct Answer is:
A
We have, `|z_(1)+z_(2)|=|z_(1)|+|z_(2)|`
`rArr |z_(1)+z_(2)|^(2)=|z_(1)|^(2)+|z_(2)|^(2)+2|z_(1)||z_(2)|`
`rArr 2|z_(1)||barz_(2)|cos(theta_(1)-theta_(2))=2|z_(1)||z_(2)|`, where `theta_(1)="arg"(z_(1)),theta_(2)="arg"(z_(2))`
`rArr cos(theta_(1)-theta_(2))=1`
`rArr theta_(1)-theta_(2) rArr "arg"(z_(1))-"arg"(z_(2))=0`
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Chapter Test
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