AIEEE 2005 Math Solved Paper

Given ω=‌

z

z−‌ 1 3 i

and |ω|=1
∴‌

|z|

|z−‌ 1 √3 i|

=|ω|
⇒‌

|z|

|z−‌ 1 √3 i ‌ ‌ |

=1
⇒|z|=|z−‌

1

√3

i

‌

‌

|........... equation (1)
|z| represent distance of z from point (0,0) and
|z−‌

1

√3

i

‌

‌

| represent distance of z from point (0,‌

1

√3

).
According to the equation (1) the distance of z from point (0,0) and (0,‌

1

√3

) is equal. Only if z is on a straight line then it will be equal distance from the both the points.