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If |z1 + z2| = |z1| + |z2| is possible i...

If `|z_1 + z_2| = |z_1| + |z_2|` is possible if :

A

`z_(2)=1`

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
`|z_(1)+z_(2)|^(2)=(|z_(1)|+|z_(2)|)^(2)`
`|z_(1)|^(2)+|z_(2)|^(2)+2|z_(1)||z_(2)|"cos"(0_(1)-0_(2))=|z_(1)|^(2)+|z_(2)|^(2)+2|z_(1)||z_(2)|`
`"cos" (0_(1)-0_(2)) =1`
`"Arg"(z_(1)) ="Arg"(z_(2))`
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