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.

If |z|=2and(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.

If z_1,z_2,z_3 are the vertices of a triangle then its centroid is

If |z_(1)|=|z_(2)|=|z_(3)| and z_(1)+z_(2)+z_(3)=0 , then z_(1),z_(2),z_(3) are vertices of

The complex numbers z_1 z_2 and z3 satisfying (z_1-z_3)/(z_2-z_3) =(1- i sqrt(3))/2 are the vertices of triangle which is (1) of area zero (2) right angled isosceles(3) equilateral (4) obtuse angled isosceles

The complex numbers z_1, z_2 and z_3 satisfying (z_1-z_3)/(z_2-z_3) =(1- i sqrt(3))/2 are the vertices of triangle which is (1) of area zero (2) right angled isosceles(3) equilateral (4) obtuse angled isosceles

bb"statement-1" " Let " z_(1),z_(2) " and " z_(3) be htree complex numbers, such that abs(3z_(1)+1)=abs(3z_(2)+1)=abs(3z_(3)+1) " and " 1+z_(1)+z_(2)+z_(3)=0, " then " z_(1),z_(2),z_(3) will represent vertices of an equilateral triangle on the complex plane. bb"statement-2" z_(1),z_(2),z_(3) represent vertices of an triangle, if z_(1)^(2)+z_(2)^(2)+z_(3)^(2)+z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1)=0

bb"statement-1" " Let " z_(1),z_(2) " and " z_(3) be htree complex numbers, such that abs(3z_(1)+1)=abs(3z_(2)+1)=abs(3z_(3)+1) " and " 1+z_(1)+z_(2)+z_(3)=0, " then " z_(1),z_(2),z_(3) will represent vertices of an equilateral triangle on the complex plane. bb"statement-2" z_(1),z_(2),z_(3) represent vertices of an triangle, if z_(1)^(2)+z_(2)^(2)+z_(3)^(2)+z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1)=0

If z_(1),z_(2),z_(3) are the vertices of an isoscles triangle right angled at z_(2) , then

If z_(1),z_(2),z_(3) are the vertices of an isoscles triangle right angled at z_(2) , then