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I want to get the modulus of following

(1+(x+I*y)/2+(x+I*y)^2/12)/(1-(x+I*y)/2+(x+I*y)^2/12)

I use

Abs[(1+(x+I*y)/2+(x+I*y)^2/12)/(1-(x+I*y)/2+(x+I*y)^2/12)]

But I always get 

                                    2
                 x + I y   (x + I y)
             1 + ------- + ----------
                    2          12
Out[52]= Abs[-------------------------]
                                     2
                 -x - I y   (x + I y)
             1 + -------- + ----------
                    2           12

Can someone help me?

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1 Answer 1

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You need to tell M that all symbols are real:

expr = (1 + (x + I*y)/2 + (x + I*y)^2/12)/(1 - (x + I*y)/
      2 + (x + I*y)^2/12);
ComplexExpand@ Abs @expr

Mathematica graphics

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  • $\begingroup$ Can you explain more about ComplexExand@ Abs @expr? I am new user of Mathematica. $\endgroup$
    – Ben
    Commented Apr 9, 2015 at 3:03
  • $\begingroup$ @Ben, the help reference.wolfram.com/language/ref/ComplexExpand.html really explains it well. Basically, if you type Abs[x + I y], then M can't do Sqrt[(x^2+y^2)] since x and y themselves can be complex numbers, each with real and imaginary parts. If that was the case, then x^2 will contains a complex value in it. So someone came up with a function to tell M to assume all symbols are real. $\endgroup$
    – Nasser
    Commented Apr 9, 2015 at 3:14

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