Use parametric complex functions?

Questions
1

Hello! I was wondering if there is a way to use parametric complex functions, i.e. giving as an input

Abs[x+iy]

get the output

Sqrt[x^2+y^2]

For example if I write Abs[1+i] I get Sqrt[2], but Abs[x+i] doesn’t work (I guess that the software doesn’t know that x is a real variable)
Thanks for the help!

2

Example:

Assuming[{x \[Element] Reals, x > 0}, Simplify[Abs[x + I]]]

returns

Abs[I + x]

instead of

Sqrt[1 + x^2]
3

ComplexExpand may be the function for your task:

Abs[x + I] // ComplexExpand
4

Thank you!