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-2i|,then prove that 3(x^2+y^2)+4(x+y)=3

If z=x+iyand |2z+1|=|z-2i|, "prove that" " " 3(x^(2)+y^(2))+4(x+y)=3 [x,y are real and I = sqrt-1 ].

If z=x+iy and |2z-1| =|z-2|then prove that x^2+y^2=1

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

If z=x+iy and |z-1|+|z+1|=4,then show that 3x^2+4y^2=12 ,where i=sqrt-1

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 |z+6|=|2z+3|, porve that x^(2)+y^(2)=9.

If cos^-1 x +cos^-1y + cos^-1z = pi and x + y + z = 3/2 , then show that x = y = z.

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 is a complex number with x, y in Q and |z| = 1 , then show that |z^(2n)-1| is a rational numberfor every n in N .