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

Explanation

We have given,

`f(z)=(7-z)/(1-z^2)` where `z=1+2i`

`\Rightarrow |z|=\sqrt{1^2+2^2}=\sqrt{5}`

`\Rightarrow f(z)=(7-z)/(1-z^2)`

`f(z)=(7-(1+2i))/(1-(1+2i)^2)`

`f(z)=(6-2i)/(4-4i)`

`f(z)=(3-i)/(2-2i)`

`f(z)=((3-i)(2+2i))/((2-2i)(2+2i))`

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