Question

Can someone help with #9 (I’m checking what I got to make sure I did these correct)

Answer 1

Given,

`f(x)=(x+1)/(2-x)`

to find,

`f(5i)=(5i+1)/(2-5i)`

let us use the conjugate property,

`\begin{gathered} (a+bi)/(c+di)\: =\: (\left(c-di\right)\left(a+bi\right))/(\left(c-di\right)\left(c+di\right)) \\ =(\left(ac+bd\right)+\left(bc-ad\right)i)/(c^2+d^2) \end{gathered}`

here,

`a=1,b=5,c=2,d=-5`
`\begin{gathered} =(\left(1\cdot\:2+5\left(-5\right)\right)+\left(5\cdot\:2-1\cdot\left(-5\right)\right)i)/(2^2+\left(-5\right)^2) \\ =(-23+15i)/(29) \\ =-(23)/(29)+i(15)/(29) \end{gathered}`

The answer is,

`-(23)/(29)+i(15)/(29)`