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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),bar(z)-bar(z)_(1)),(z_(2)-z_(1),bar(z)_(2)-bar(z)_(1))|=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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