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_1Im(bar(z_2)z_3) +z_2Im(bar(z_3)z_1) + z_3 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 .

If z_1,z_2,z_3 are three complex number then prove that z_1Im(barz_2.z_3)+z_2Im(barz_3.z_1)+z_3Im(barz_1.z_2)=0

If z_(1), z_(2),z_(3) ,are three complex numbers, prove that z_(1).Im(barz_(2)z_(3))+z_(2).Im(barz_(3)z_(1))+z_(3)Im(bar z_(1)z_(2))=0 where Im(W) = imaginary part of W,where W is a complex number.

For any two complex numbers z_1 and z_2 , prove that Re(z_1z_2)=Re(z_1) Re(z_2)-Im(z_1) Im(z_2) .

For any two complex numbers z_(1)" and "z_(2) prove that Im(z_(1)z_(2))=Re(z_1) Im(z_2)+ Im(z_1)Re(z_2) .

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

If z_(1) , z_(2) , z_(3) are any three complex numbers on Argand plane, then z_(1)(Im(barz_(2)z_(3)))+z_(2)(Imbarz_(3)z_(1)))+z_(3)(Imbarz_(1)z_(2))) is equal to

For any two complex numbers z_1 and z_2 prove that Re(z_1z_2) = Re(z_1)Re(z_2) - Im(z_1)Im(z_2)