Identify locus `z` if `R e(z+1)=|z-1|`

Identify the locus of z if bar(z)=bar(a)+(r^(2))/(z-a)

Find the locus of z if arg ((z-1)/(z+1))= pi/4

What is the locus of w if w=(3)/(z) and |z-1|=1?

The locus of z such that log_(1/2)|z-1|>log_(1/2)|z-i| is

Locus of z in the following curves: Im(z)=|z-(1+2i)| and 4-Im(z)=|z-(1+2i)| represent A and B respectively. If locus of z in arg (z-(1+2i))=theta intersect A and B at points P(z_(1)) and Q(z_(2)) respectively, then minimum value of |z_(1)-(1+2i)||z_(2)-(1+2i)| is: (Re(z_(1))+Re(z_(2))!=2)

The locus of z given by |(z-1)/(z-iota)|=1 is a(n)

Statement-1 : The locus of z , if arg((z-1)/(z+1)) = pi/2 is a circle. and Statement -2 : |(z-2)/(z+2)| = pi/2 , then the locus of z is a circle.

What is the locus of z if |z-cos^(-1)cos12|-|z-sin^(-1)sin12||=8(pi-3)?

The locus of z such that (z^(2))/(z-1) is always real is