The-locus-of-z-given-by-z-1-z-i-1-is-

Question Number 19732 by Tinkutara last updated on 15/Aug/17

The locus of z given by ∣ \frac{z - 1}{z - i} ∣ = 1 is

Answered by ajfour last updated on 15/Aug/17

z lies on perpendicular bisector

of line joining z = 1 and z = i that

passes through origin .

So, y = x

\frac{z - \bar{z}}{2 i} = \frac{z + \bar{z}}{2} or z - \bar{z} = iz + i \bar{z}

or (1 - i) z - (1 + i) \bar{z} = 0

multipying by i we get

(1 + i) z + (1 - i) \bar{z} = 0 .

Commented by Tinkutara last updated on 15/Aug/17

Thank you very much Sir!