If `alpha+ibeta=tan^(-1) (z), z=x+iy` and `alpha` is constant, the locus of 'z' is

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

If (pi)/(8)+i beta=cot^(-1)(z) where z=x+iy then the locus of z is

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

If the imaginary part of the complex number (z-1)(cos alpha-i sin alpha)+(z-1)^(-1)(cos alpha+i sin alpha) is zero,then which of the following options are correct? a) |z|=1 b) |z-1|=1 c) arg (z)=alpha d) arg (z-1)=alpha

if Amp((z+2)/(z-4i))=(pi)/(2), then the locus of z=x+iy is