If z(1),z(2) and z(3),z(4) are two pairs...

If `z_(1),z_(2)` and `z_(3),z_(4)` are two pairs of conjugate complex numbers then arg`((z_(1))/(z_(4)))+arg((z_(2))/(z_(3)))` equals

A

`(pi)/2`

B

`pi`

C

`(3pi)/2`

D

0

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The correct Answer is:

D

`arg(z_(1)//z_(4))+arg(z_(2)//z_(3))=(arg_(1)-argz_(4))+(argz_(2)-argz_(3))=(argz_(1)+argz_(2))-(argz_(3)+argz_(4)=0`

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arg(z_(1)z_(2))=arg(z_(1))+arg(z_(2))