`z_1 , z_2 and z_3` are complex numbers then show ` ( z_1 + z_2 ) + z_3` = ` z_1 + ( z_2 + z_3 )`

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 z_1, z_2, z_3 are three complex, numbers and A=[[a r g z_1,a r g z_3,a r g z_3],[a r g z_2,a r g z_2,a r g z_1],[a r g z_3,a r g z_1,a r g z_2]] Then A divisible by a r g(z_1+z_2+z_3) b. a r g(z_1, z_2, z_3) c. all numbers d. cannot say

Let z_(1), z_(2), z_(3) be three complex numbers such that |z_(1)| = |z_(2)| = |z_(3)| = 1 and z = (z_(1) + z_(2) + z_(3))((1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))) , then |z| cannot exceed