If `z_1,z_2,z_3` be three non-zero complex number, such that `z_2 != z_1,a=|z_1|,b=|z_2| and c=|z_3|` suppose that `|(a,b,c),(b,c,a),(c,a,b)|=0,` then arg `((z_3)/(z_2))` is equal to

Let z_1, z_2, z_3 be the three nonzero complex numbers such that z_2!=1,a=|z_1|,b=|z_2|a n d c=|z_3|dot Let |(a, b, c), (b, c, a), (c,a,b) |=0 a r g(z_3)/(z_2) equal to (a) arg((z_3-z_1)/(z_2-z_1))^2 (b) orthocentre of triangle formed by z_1, z_2, z_3, i sz_1+z_2+z_3 (c)if triangle formed by z_1, z_2, z_3 is equilateral, then its area is (3sqrt(3))/2|z_1|^2 (d) if triangle formed by z_1, z_2, z_3 is equilateral, then z_1+z_2+z_3=0

z_1, z_2, z_3 are three non-zero complex numbers such that z_2 ne z_1, and a = |z_1|, b = |z_2|, c= |z_3|. If abs{:(a,b, c),(b, c, a),(c, a, b):}=0 , then show that arg. (z_3)/(z_2)="arg" ((z_3-z_1)/(z_2 - z_1))^2 .

Let z_(1),z_(2),z_(3) be the three nonzero comple numbers such that z_(1) ne 1, a= |z_(1)|, b = |z_(2)| and c= |z_(3)| . Let |{:(,a,b,c),(,b,c,a),(,c,a,b):}|= 0 Then

Let z_1, z_2, z_3 be the three nonzero complex numbers such that z_2!=1,a=|z_1|,b=|z_2|a n d c=|z_3|dot Let |a b c b c a c a b|=0 a r g(z_3)/(z_2)=a r g((z_3-z_1)/(z_2-z_1))^2 orthocentre of triangle formed by z_1, z_2, z_3, i sz_1+z_2+z_3 if triangle formed by z_1, z_2, z_3 is equilateral, then its area is (3sqrt(3))/2|z_1|^2 if triangle formed by z_1, z_2, z_3 is equilateral, then z_1+z_2+z_3=0

If z_1 and z_2 , are two non-zero complex numbers such tha |z_1+z_2|=|z_1|+|z_2| then arg(z_1)-arg(z_2) is equal to

If z_1 and z_2 are two non-zero complex numbers such that abs(z_1+z_2) = abs(z_1)+abs(z_2) , then arg(z_1)-arg(z_2) is equal to

If z_(1)" and "z_(2) are two non-zero complex numbers such that |z_(1)+z_(2)|=|z_1|+|z_(2)| , then arg ((z_1)/(z_2)) is equal to

If z_(1) and z_(2) are two non-zero complex numbers such that |z_(1) + z_(2)| = |z_(1)| + |z_(2)| , then arg ((z_(1))/(z_(2))) is equal to a)0 b) -pi c) -(pi)/(2) d) (pi)/(2)