Let z(1) and z(2) be two distinct comple...

Let `z_(1)` and `z_(2)` be two distinct complex numbers and `z=(1-t)z_(1)+iz_(2)`, for some real number t with `0 lt t lt 1` and `i=sqrt(-1)`. If arg(w) denotes the principal argument of a non-zero compolex number w, then

A

`|z - z_(1)| + |z- z_(2) |= |z_(1)- z_(2)|`

B

`arg(z- z_(1)) = arg (z - z_(2))`

C

`|{:(z - z_(1) , barz - barz_(1)),(z_(2) - barz_(1) , barz_(2) - barz_(2)):}|=0`

D

` arg (z - z_(1)) = arg (z_(2) - z_(1))`

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The correct Answer is:

A, C, D

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