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.

The equation bar(z)=bar(z_(0))+A(z-z_(0)) where A is a constant,and if m is the slope of the straight line then A is

If z is a complex number and z=bar(z) , then prove that z is a purely real number.

If z(bar(z+alpha))+barz(z+alpha)=0 , where alpha is a complex constant, then z is represented by a point on

If omega is any complex number such that z omega = |z|^2 and |z - barz| + |omega + bar(omega)| = 4 then as omega varies, then the area bounded by the locus of z is