Let `A,B,C` are `3` points on the complex plane represented by complex number `a,b,c` respectively such that `|a|= |b|= |c|=1,a+b+c = abc=1`, then

Let a,b,c be three distinct complex numbers such that |a|=|b|=|c|=|b+c-a|=1 then 3-|b+c| is equal to

Let A,B, C,D be four concyclic points in order in which AD:AB=CD: CB. If A,B,C are representing by complex numbers a,b,c respectively find the complex number associated with point D.

if a,b,c are complex numbers such that a+b+c=0 and |a|=|b|=|c|=1 find the value of 1/a+1/b+1/c

if a,b,c are complex numbers such that a+b+c=0 and |a|=|b|=|c|=1 find the value of 1/a+1/b+1/c

Let A, B, C, D and E be points on the complex plane, which respectively represent the complex numbers z_1,z_2,z_3, z_4 and z_5 . If (z_3 - z_2)z_4 =(z_1- z_2)z_5 , prove that the triangles ABC and DOE are similar.

If a, b, c are complex numbers satisfying a+b+c=0 and a^2+b^2+c^2=0 then show that |a|=|b|=|c|.

Let the points A, B, C and D are represented by complex numbers Z_(1), Z_(2),Z_(3) and Z_(4) respectively, If A, B and C are not collinear and 2Z_(1)+Z_(2)+Z_(3)-4Z_(4)=0 , then the value of ("Area of "DeltaDBC)/("Area of "DeltaABC) is equal to

Let the points A, B, C and D are represented by complex numbers Z_(1), Z_(2),Z_(3) and Z_(4) respectively, If A, B and C are not collinear and 2Z_(1)+Z_(2)+Z_(3)-4Z_(4)=0 , then the value of ("Area of "DeltaDBC)/("Area of "DeltaABC) is equal to

A, B, C are the points representing the complex numbers z_1, z_2, z_3 respectively on the complex plane and the circumcentre of the triangle ABC lies at the origin. If the altitude AD of the triangle ABC meets the circumcircle again at P, then P represents the complex number