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If z(1)" and "z(2) are two non-zero comp...

If `z_(1)" and "z_(2)` are two non-zero complex numbers such that `|z_(1)+z_(2)|=|z_1|+|z_(2)|`, then `arg z_(1)- arg z_(2)` is equal to

A

`-pi`

B

`-pi/2`

C

0

D

`pi/2`

Text Solution

Verified by Experts

The correct Answer is:
C
Given `|z_1+z_2|=|z_1|+|z_2|`
On squaring both sides ,we get
`|z_1|^2 + |Z_2|^2+2|z_1||z_2|cos (arg z_1 - arg z_2)=|z_1|^2|z_2|^2+2|z_1||z_2|`
` rArr 2|z_1||z_2|cos (arg z_1-arg z_2)=2|z_1|z_2|`
`rArr cos(arg z_1 - arg z_2)=1`
`rArr arg(z_1)aargz_2)=0`
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