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

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

Identify the locus of z if z = a +(r^2)/(z-a),> 0.

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

Find the locus of z if omega= (z)/(z- (1)/(3)i), |omega| =1

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.

Complex numbers z satisfy the equaiton |z-(4//z)|=2 Locus of z if |z-z_(1)| = |z-z_(2)| , where z_(1) and z_(2) are complex numbers with the greatest and the least moduli, is

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

Find the locus of z satisfying |(z-3)/(z+1)|=3 in the complex plane.

Let z_1=3 and z_2=7 represent two points A and B respectively on complex plane . Let the curve C_1 be the locus of pint P(z) satisfying |z-z_1|^2 + |z-z_2|^2 =10 and the curve C_2 be the locus of point P(z) satisfying |z-z_1|^2 + |z-z_2|^2 =16 The locus of point from which tangents drawn to C_1 and C_2 are perpendicular , is :

If z is any complex number such that |3z-2|+|3z+2|=4 , then identify the locus of zdot