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if (5z2)/(7z1) is purely imaginary numb...

if `(5z_2)/(7z_1) ` is purely imaginary number then `|(2z_1+3z_2)/(2z_1-3z_2) |` is equal to

A

`5//7`

B

`7//9`

C

`25/49`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
It is given that
`(5z_(2))/(7z_(1))` is purely imaginary
`rArr (5z_(2))/(7z_(1))=ki`, where `k in R`.
`rArr z_(2)/z_(1) = (7ki)/(5)`
Now, `|(2z_(1)+3z_(2))/(2z_(1)-3z_(2))|=|(2+3(z_(2)//z_(1)))/(2-3(z_(2)//z_(1)))|=|(2+3 xx (7//5)ki)/(2-3 xx (7//5)ki)|`
`rArr |(2z_(1)+3z_(2))/(2z_(1)-3z_(2))|=|(10+21ki)/(10-21ki)|=1`
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