In the Argands plane what is the locus of `z(!=1)` such that `a rg{3/2((2z^2-5z+3)/(2z^2-z-2))}=(2pi)/3dot`

What is the locus of z, if amplitude of (z-2-3i) is (pi)/(4)?

If z_(1),z_(2),z_(3),z_(4) are the affixes of four point in the Argand plane,z is the affix of a point such that |z-z_(1)|=|z-z_(2)|=|z-z_(3)|=|z-z_(4)| ,then prove that z_(1),z_(2),z_(3),z_(4) are concyclic.

If |z+2+3i|=5 then the locus of z is

If z_(1), z_(2) and z_(3) are the vertices of a triangle in the argand plane such that |z_(1)-z_(2)|=|z_(1)-z_(3)| , then |arg((2z_(1)-z_(2)-z_(3))/(z_(3)-z_(2)))| is

If A(z_(1)) and A(z_(2)) are two fixed points in the Argand plane and a point P(z) moves in the Argand plane in such a way that |z-z_(1)|=|z-z_(2)| , then the locus of P, is

If A(z_(1)) and B(z_(2)) are two fixed points in the Argand plane the locus of point P(z) satisfying |z-z_(1)|+|z-z_(2)|=|z_(1)-z_(2)| , is

The focus of the complex number z in argand plane satisfying the inequality log_((1)/(2))((|z-1|+4)/(3|z-1|-2))>1(where|z-1|!=(2)/(3))

A(z_(1)) and B(z_(2)) are two fixed points in the Argand plane and a point P(z) moves in the plane such that |z-z_(1)|+|z-z_(2)| = Constant (ne|z_(1)-z_(2)|) , then the locus of P, is