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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)/(z_2))` is equal to

A

`1 + omega`

B

`1+ omega^(2)`

C

`omega`

D

`omega^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C, D
`|z_(1) + z_(2)|=|z_(1)|= |z_(2)|`
Thus angle between `z_(1)` and `z_(2)` is `120^(@)`
`therefore (z_(1))/(z_(2)) = omega or omega^(2)`
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