If `((3-z_1)/(2-z_1))((2-z_2)/(3-z_2))=k(k >0)` , then prove that points `A(z_1),B(z_2),C(3),a n dD(2)` (taken in clockwise sense) are concyclic.

If z_1=i z_2 and z_1-z_3=i(z_3-z_2) ,then prove that |z_3|=sqrt(2)|z_1|.

If |z|=2a n d(z_1-z_3)/(z_2-z_3)=(z-2)/(z+2) , then prove that z_1, z_2, z_3 are vertices of a right angled triangle.

, 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|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

Show that if z_(1)z_(2)+z_(3)z_(4)=0 and z_(1)+z_(2)=0 ,then the complex numbers z_(1),z_(2),z_(3),z_(4) are concyclic.

If z_1^2+z_2^2-2z_1.z_2.costheta= 0 prove that the points represented by z_1, z_2 , and the origin form an isosceles triangle.

If a r g["z"_1("z"_3-"z"_2)]="a r g"["z"_3("z"_2-"z"_1)] , then find prove that O ,z_1, z_2, z_3 are concyclic, where O is the origin.

Let z_1 , z _2 and z_3 be three complex numbers such that z_1 + z_2+ z_3 = z_1z_2 + z_2z_3 + z_1 z_3 = z_1 z_2z_3 = 1 . Then the area of triangle formed by points A(z_1 ), B(z_2) and C(z_3) in complex plane is _______.

if A(z_1),B(z_2),C(z_3),D(z_4) lies on |z|=4 (taken in order) , where z_1+z_2+z_3+z_4=0 then :

If kgt1,|z_1|,k and |(k-z_1barz_2)/(z_1-kz_2)|=1 , then (A) z_2=0 (B) |z_2|=1 (C) |z_2|=4 (D) |z_2|ltk