[" On the argand plane,let "],[alpha=-2+3z,beta=-2-3z" and "|z|=1" ,then :- "]

On the Argand plane ,let z_(1) = - 2+ 3z,z_(2)= - 2-3z and |z| = 1 . Then

On the Argand plane ,let z_(1) = - 2+ 3z,z_(2)= - 2-3z and |z| = 1 . Then (a) z 1 moves on circle with centre at ( − 2 , 0 ) and radius 3 (b) z 1 and z 2 describle the same locus (c) z 1 and z 2 move on differenet circles (d) z 1 − z 2 moves on a circle concetric with | z | = 1

Suppose that Z_(1),Z_(2),Z_(3), are three vertices of an equilateral triangle in the argand plane.Let alpha=(1)/(2)(sqrt(3)+i) and beta, be an non-zero complex number.The points alpha z_(1)+beta,alpha z_(2)+beta,alpha z_(3)+beta will be

Suppose that z_1, z_2, z_3 are three vertices of an equilateral triangle in the Argand plane let alpha=1/2(sqrt3+i) and beta be a non zero complex number the point alphaz_1+beta,alphaz_2+beta,alphaz_3+beta wil be

Suppose that z_(1), z_(2), z_(3) are three vertices of an equilateral triangle in the Argand plane. Let alpha=(1)/(2) (sqrt(3) +i) and beta be a non-zero complex number. The point alphaz_(1) +beta, alpha z_(2)+beta, az_(3)+beta will be

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

, a point 'z' is equidistant from three distinct points z_(1),z_(2) and z_(3) in the Argand plane. If z,z_(1) and z_(2) are collinear, then arg (z(z_(3)-z_(1))/(z_(3)-z_(2))). Will be (z_(1),z_(2),z_(3)) are in anticlockwise sense).

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 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