Let z be a complex number satisfying `|z| = 3 |z-1|`. Then prove that `|z-(9)/(8)| = (3)/(8)`

Explanation

Let `z = x + iy`
Now, `|z| = 3|z-1|`
`rArr|z|^(2) = 9|z-1|^(2)`
`rArr |x+iy|^(2) = 9|(x -1)+iy|^(2)`
`rArr x^(2) +y^(2) = 9 [(x-1)+iy|^(2)`
`rArr 8x^(2) + 8y^(2) - 18x x + 9 = 0`
`rArr (x-(9)/(8))^(2) + y^(2) =(9)/(64)`
`rArr |(x-(9)/(8)) + iy| =(3)/(8)`
`rArr |z-(9)/(8)| = (3)/(8)`