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 `z_1, z_2, z_3, z_4` are

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_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| = |z-z_(2)|

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| - |z-z_(2)|= |z_(1)-z_(2)|

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| + |z-z_(2)| = |z_(1)-z_(2)|

If |z_1|=|z_2|=|z_3|=......=|z_n|=1 , then |z_1+z_2+z_3+......+z_n|=

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)|-|z-z_(2)|= constant (ne |z_(1)-z_(2)|)

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)|= k|z-z_(2)|, k in R^(+), k ne 1

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| + |z-z_(2)| = constant ne (|z_(1)-z_(2)|)

Statement-1: If z_(1),z_(2) are affixes of two fixed points A and B in the Argand plane and P(z) is a variable point such that "arg" (z-z_(1))/(z-z_(2))=pi/2 , then the locus of z is a circle having z_(1) and z_(2) as the end-points of a diameter. Statement-2 : arg (z_(2)-z_(1))/(z_(1)-z) = angleAPB

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