For any complex numbers `z_1,z_2 and z_3, z_3 Im(bar(z_2)z_3) +z_2Im(bar(z_3)z_1) + z_1 Im(bar(z_1)z_2)` is

For any complex numbers z_(1),z_(2) and z_(3),z_(3)Im(bar(z_(2))z_(3))+z_(2)Im(bar(z_(3))z_(1))+z_(1)Im(bar(z_(1))z_(2)) is

For any three complex numbers z_1, z_2 and z_3 , prove that z_1 lm (bar(z_2) z_3)+ z_2 lm (bar(z_3) z_1) + z_3lm(bar(z_1) z_2)=0 .

For any two non zero complex numbers z_(1) and z_(2) if z_(1)bar(z)_(2)+z_(2)bar(z)_(1)=0 then amp(z_(1))-amp(z_(2)) is

For two unimodular complex numbers z_1 and z_2, then [(bar z_1,-z_2),(bar z_2,z_1)]^-1[(z_1,z_2),(bar (-z_2),bar z_1)]^-1 is equal to

For two unimobular complex numbers z_(1) and z_(2) , find [(bar(z)_(1),-z_(2)),(bar(z)_(2),z_(1))]^(-1) [(z_(1),z_(2)),(-bar(z)_(2),bar(z)_(1))]^(-1)

Let z_(1), z_(2), z_(3) be three non-zero complex numbers such that z_(1) bar(z)_(2) = z_(2) bar(z)_(3) = z_(3) bar(z)_(1) , then z_(1), z_(2), z_(3)

For any three complex numbers z_(1),z_(2),z_(3) , if Delta=|{:(1,z_(1),bar(z_(1))),(1,z_(2),bar(z_(2))),(1,z_(3),bar(z_(3))):}| , then

For any complex number z prove that |Re(z)|+|Im(z)|<=sqrt(2)|z|

Im ((1) / (z_ (1) bar (z) _ (1)))