If `z=x+iy and |z-1|^(2)+|z+1|^(2)=4,` determine the position of the point z in the complex plane.

If z=x+iy and |z-3|/|z+3|=2, find the position of the point z in the Argand diagram.

If the imageinary part of ( 2z+1)/( I z +1) is -2 then the locus of the point representing z in the complex plane is

If the real part of (z +2)/(z -1) is 4, then show that the locus of he point representing z in the complex plane is a circle.

If the real part of (z+2)/(z-1) is 4, then show that the locus of he point representing z in the complex plane is a circle.

If p represent z=x+iy in the argand plane and |z-1|^(2)+|z+1|^(2)=4 then the locus of p is

A(z_(1)) and B(z_(2)) are two given points in the complex plane. The locus of a point P(z) in the complex plane satisfying |z-z_(1)|-|z-z_(2)| ='|z1-z2 |, is

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