Let `z_1, z_2,z_3` be three distinct complex numbers satisfying `|z_1- 1|=|z_2 - 1|= |z_3-1|`.If `z_1+z_2+z_3=3` then `z_1,z_2,z_3` must represent the vertices of

If 2z_1-3z_2 + z_3=0 , then z_1, z_2 and z_3 are represented by

Let z_1,z_2 and z_3 be three distinct complex numbers , satisfying |z_1|=|z_2|=|z_3|=1 find maximum value of| z1 - z2 |^2 + |z2-z3|^2 + |z3-z1|^2

Let z_(1),z_(2),z_(3),z_(4) are distinct complex numbers satisfying |z|=1 and 4z_(3) = 3(z_(1) + z_(2)) , then |z_(1) - z_(2)| is equal to

If |z_1-1|<1 , |z_2-2|<2 , |z_3-3|<3 then |z_1+z_2+z_3|

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 complex numbers such that |z_1|=|z_2|=|z_3|=|1/z_1+1/z_2+1/z_3|=1 then |z_1+z_2+z_3| is equal to

If z_1,z_2, z_3 are complex numbers such that |z_1|=|z_2|=|z_3|=|1/z_1+1/z_2+1/z_3|=1 then |z_1+z_2+z_3| is equal to

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 _______.

Let z_(1),z_(2) and z_(3) be three complex number such that |z_(1)-1|= |z_(2) - 1| = |z_(3) -1| and arg ((z_(3) - z_(1))/(z_(2) -z_(1))) = (pi)/(6) then prove that z_(2)^(3) + z_(3)^(3) + 1 = z_(2) + z_(3) + z_(2)z_(3) .

If |z_1=1,|z_2|=2,|z_3|=3 and |z_1+z_2+z_3|=1, then |9z_1z_2+4z_3z_1+z_2z_3| is equal to