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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 let `z=(1-t)z_(1)+tz_(2)` for some real number `t` with `0 lt t lt 1`. If Arg`(w)` denotes the principal argument of a non zero complex 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)-z_(1),barz_(2)-barz_(1)):}|=0`

D

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

Text Solution

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The correct Answer is:
A, C, D
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