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If (x-alpha)/(z+alpha)(alpha in R) is a ...

If `(x-alpha)/(z+alpha)(alpha in R)` is a purely imaginery number and `|z|=2`, then a value of `alpha` is

A

`sqrt(2)`

B

`1/2`

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
Since the complex number `(z-a)/(z+a)(alpha ne R)`j is purely imaginary number therefore
`(z-alpha)/(z+alpha)+(barz-alpha)/(bar z + alpha)=0 " "[ therefore alpha in R]`
`rArr zbarz-abarz+az-alpha^2+zbarz-alphabarz-alpha^2=0`
`rArr 2|z|^2-2alpha^2=0" "[because zbarz=|z|^2]`
`rArr alpha^2=|z|^2=4`
`rArr alpha=pm2`
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