The equation `|z-i|=|z-1|,i= sqrt(-1)`represents

Options

A. a circule of radius `1/2`
B. the line passing through the origin with slope 1
C. a cicle of radius 1
D. the line passing the origin with slope-1

Answer

B

Explanation

Let the complex nuber z = x+ iy
Also given |z-i|=|z-1|
`rArr | x+iy -I |=|x+ iy -1|`
`rArr sqrt(x^2+(y-1)^2=sqrt((x-1)^2+y^2)`
`[therefore|z| = sqrt((Re(z))^2+Im(z)^2)]`
On squaring both sides , we get
`x^2+y^2-2y+1=x^2+y^22x+1`
`rArr y= x` which of the represents a line through the origin with slope 1.