The expression `((x-i)(3+i)(i-1))/((1+i)(3-i))` has to be simplified.

`((x-i)(3+i)(i-1))/((1+i)(3-i))`

= `((x-i)(3+i)(i-1)(1 - i)(3+i))/((1+i)(3-i)(1-i)(3+i))`

= `((x-i)(3+i)(i-1)(1 - i)(3+i))/((1 + 1)(9 + 1))`

= `((x-i)(3+i)(i-1)(1 - i)(3+i))/20`

= `(-(x-i)(3+i)^2(i-1)^2)/20`

= `(-(x-i)(9 - 1 + 6i)(-1 + 1 - 2i))/20`

= `(-(x-i)(8 + 6i)(- 2i))/20`

= `((x-i)(16i + 12i^2))/20`

= `((x-i)(16i - 12))/20`

= `((x-i)(4i - 3))/5`

= `(4x*i - 4i^2 - 3x + 3i)/5`

= `(4x*i + 4 - 3x + 3i)/5`

**The simplified form of `((x-i)(3+i)(i-1))/((1+i)(3-i)) = (4x*i + 4 - 3x + 3i)/5`**

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