regarding result form : abs value of complex number

[aiden]

Hi I'm newbie Hp prime.
I have a question about result form such as the abs value of complex number. Let me give a simple example for your understanding.

Q. abs of (1-i*x)/(1+i*x) ? where i is imaginary numbers.
Please see comparison results i attached.
On left, it gives very complex result using IM(x), RE(x) so on
On right, it gives simple answer i expected.

And, in case of TI nspire, it returns '1' as answer.

I don't know why they give different answers Please help me out to understand this situation and give the way to transfer complex answer to simple answer such as virtual calculator's or TI's.