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If z1,z2,z3 are three complex number the...

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`

A

`0`

B

`z_(1)+z_(2)+z_(3)`

C

`z_(1)z_(2)z_(3)`

D

`((z_(1)+z_(2)+z_(3))/(z_(1)z_(2)z_(3)))`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `z_(1)((barz_(2)z_(3)-z_(2)barz_(3))/(2i))+z_(2)((barz_(3)z_(1)-z_(3)barz_(1))/(2i))+z_(3)((barz_(1)z_(2)-z_(1)barz_(2))/(2i))=(1)/(2i)xx0=0`
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