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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)+tz_(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 complex number w, then
a. `abs(z-z_(1))+abs(z-z_(2))=abs(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))`

A

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

Text Solution

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The correct Answer is:
A:B:C, D
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