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If z(1)=2+3i, z(2)=3-2i and z(3)=-1-2sqr...

If `z_(1)=2+3i, z_(2)=3-2i and z_(3)=-1-2sqrt3i`, then which of the following is true? (where, `i^(2)=-1`)

A

`arg((z_(2))/(z_(3)))=arg((z_(2)-z_(1))/(z_(3)-z_(1)))`

B

`arg((z_(2))/(z_(3)))=arg((z_(3))/(z_(1)))`

C

`(1)/(2)arg((z_(2))/(z_(3)))=arg((z_(2)-z_(1))/(z_(3)-z_(1)))`

D

`2arg((z_(3))/(z_(2)))=arg((z_(3)-z_(1))/(z_(2)-z_(1)))`

Text Solution

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The correct Answer is:
C
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