z is a complex number such that the ratio z-i/z-1 is purely imaginary. Prove that z lies on a circle whose centre is at a point 1/2 + 1/2 i and whose radius is 1/v2( 1 divided by square root of 2)

Hence from conjugate property of
̅

(
̅̅ ̅̅ ̅̅ ̅
)




( ̅̅ ̅̅ ̅̅ )
( ̅̅ ̅̅ ̅̅ ̅ )
( (


̅̅̅̅
)
( ̅̅̅̅ )
( ̅̅̅̅ )
)




( ̅ )
( ̅ )
( ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅ ̅̅̅̅ ̅̅̅̅ )
( ) ( ̅ ) ( ̅ ) ( )
( ) ( ̅ )

̅ ̅ ̅ ̅
( ) ( ̅ )
̅ ( ) ( ) ̅
̅
( )


( )

̅
Comparing it...