1.

If zis a complex number, then `|3z-1|=3|z-2|` represents

Answer» Let `z = x+iy`
Then, `|3(x+iy)-1| = 3|x+iy-2|`
`=>|(3x-1)+3iy| = 3|(x-2)+iy|`
`=>sqrt((3x-1)^2+(3y)^2) = 3sqrt((x-2)^2+y^2)`
Now, squaring both sides,
`=>(3x-1)^2+(3y)^2 = 9((x-2)^2+y^2)`
`=>9x^2+1- 6x +9y^2 = 9x^2+36-36x+9y^2`
`=> 30x = 35`
`=> x = 7/6`
This is an equation of a line parallel to `y`-axis.
So, option - `(d)` is the correct option.


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