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 Re ((z + 1)/(z-i)) = 0 where z = x + iy

P represents the variable complex number z find the locus of z if : Re((z+1)/(z+i))=1

Find the locus of z if Re ((bar(z) + 1)/(bar(z) - i)) = 0.

Find the locus of z if |3z - 5 | = 3 |z + 1| where z = x + iy

P represents the variable complex number z. Find the locus of P, if Im ((2z + 1)/(iz + 1)) = -2 .

If z= x+iy find the locus of z if |2z+1| = 2 .

What is the locus of z if ||z-cos^(-1)cos12|-|z-sin^(-1)sin 12||=8(pi-3)?

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