If `z=z_0+A( bar z -( bar z _0)), w h e r eA` is a constant, then prove that locus of `z` is a straight line.

If |z-3+i|=4 , then the locus of z is

If |z-1|=2 then the locus of z is

If |z-1|=|z-3| then the locus of z is

If |(z-i)/(z+i)|=1 , then the locus of z is

If z = x + iy, then z bar(z) =

The locus of point z satisfying R e(1/z)=k ,w h e r ek is a nonzero real number, is a. a straight line b. a circle c. an ellipse d. a hyperbola

If z_1, z_2, z_3 are three nonzero complex numbers such that z_3=(1-lambda)z_1+lambdaz_2w h e r elambda in R-{0}, then prove that points corresponding to z_1, z_2a n dz_3 are collinear .

If w=z/[z-(1/3)i] and |w|=1, then find the locus of z

If |z-z_(1)|=|z-z_(2)| then the locus of z is :

If z!=0 is a complex number, then prove that R e(z)=0 rArr Im(z^2)=0.