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It is given that complex numbers z1 and ...

It is given that complex numbers `z_1` and `z_2` satisfy `|z_1|=2 `and `|z_2|=3.` If the included angled of their corresponding vectors is `60^0` , then find the value of `19|(z_1-z_2)/(z_1+z_2)|^2` .

A

`5`

B

`6`

C

`7`

D

`8`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )`
`OC=|z_(1)+z_(2)|` and `AB=|z_(1)-z_(2)|`
`|z_(1)+z_(2)|=sqrt(|z_(1)|^(2)+|z_(2)|^(2)-2|z_(1)||z_(2)|cos120^(@))`
`=sqrt(4+9+2.3)=sqrt(19)`
and `|z_(1)-z_(2)|=sqrt(|z_(1)|^(2)+|z_(2)|^(2)-2|z_(1)||z_(2)|cos60^(@))`
`=sqrt(4+9-6)=sqrt(7)`
`:.|(z_(1)-z_(2))/(z_(1)+z_(2))|=sqrt((7)/(19))`
`:.19|(z_(1)-z_(2))/(z_(1)+z_(2))|^(2)=7`
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