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If f(z)=(7-z)/(1-z^2), where z=1+2i , th...

If `f(z)=(7-z)/(1-z^2)`, where `z=1+2i ,` then `|f(z)|` is

A

`(|z|)/(2)`

B

`|z|`

C

`2|z|`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let z = 1 + 2i
`rArr |z|= sqrt( 1+ 4 ) = sqrt(5)`
Now. `f(z) = (7-z)/(1-z^(2))=(7-1-2i)/(1-(1+2i)^(2))`
`(6-2i)/(1-1-4i^(2)-4i)=(6-2i)/(4-4i)`
`((3-i)(2+2i))/((2-2i)(2+2i))`
`(6-2i+6i-2i^(2))/(4-4i^(2))=(6+4i+2)/(4+4)`
`(8+4i)/(8)=1+(1)/(2)i`
`f(z) = 1 + (1)/(2)i`
` :. |f(z)|=sqrt( 1+(1)/(4))=sqrt((4+1)/4)=sqrt(5)/(2) = (|z|)/(2)`
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