If x,y,b and real, z=x+iy and `(z-i)/(z-1)=ib,` show that,
`(x-(1)/(2))^(2)+(y-(1)/(2))^(2)=(1)/(2).`

If z = x + iy and arg ((z-1)/(z+1))=pi/2 , show that x^(2)+y^(2)-1=0 .

If z=x+iy and |z-1|+|z+1|=4 show that 3x^(2)+4y^(2)=12

If z=x+iy and |z-1|+|z+1|=4, "show that" 3x^(2)+4y^(2)=12 (i=sqrt(-1)).

If z = x + iy and |2z+1|=|z-2i| ,then show that 3(x^(2)+y^(2))+4(x+y)=3

If z=x+iy and |2z-1|=|z-2|," prove that" " " x^(2)+y^(2)=1.

If x,y,z are distinct real numbers then the value of ((1)/(x-y))^(2)+((1)/(y-z))^(2)+((1)/(z-x))^(2) is

If x,y,z are all different real numbers,then prove that (1)/((x-y)^(2))+(1)/((y-z)^(2))+(1)/((z-x)^(2))=((1)/(x-z)+(1)/(y-z)+(1)/(z-x))^(2)

If z=x+iy and real part ((z-1)/(2z+i))=1 then locus of z is

If z=x+iy and |2z+1|=|z-3| ,then show that 3x^2+3y^2+10x=8 .