Complex conjugation and mod of a complex expression

Questions
1

Hello All
I am doing an analytical calculation with a bit longer expression which is complex in nature.

Mp =-(1/((mb + mc) (mB + mDs) q))
 Sqrt[1 - ml^2/
   q^2] (-2 A0 E^(-I \[Chi]) (mB + mDs) (-((-1 + gA) (mb + mc) ml) + 
       gP q^2) Sqrt[\[Lambda]Ds] + 
    16 E^(-I \[Chi])
      mB (mb + 
       mc) mDs (A12 (-1 + gA) (mB + mDs) ml + (gT - gT5) q^2 T23) Cos[
      thl] + Sqrt[2]
      E^(-2 I \[Chi]) (mb + mc) q (-A1 (-1 + gA) (mB + mDs)^2 ml - 
       2 (gT - gT5) (mB + mDs) (mB^2 T2 - mDs^2 T2 + 
          T1 Sqrt[\[Lambda]Ds]) - (1 + 
          gV) ml V Sqrt[\[Lambda]Ds]) Sin[thl] + 
    Sqrt[2] (mb + mc) q (-A1 (-1 + gA) (mB + mDs)^2 ml - 
       2 (gT - gT5) (mB + mDs) (mB^2 T2 - mDs^2 T2 - 
          T1 Sqrt[\[Lambda]Ds]) + (1 + 
          gV) ml V Sqrt[\[Lambda]Ds]) Sin[thl])

Then I take the complex conjugate of Mp as

CMp = Conjugate[Mp] // FullSimplify

I want to find the absolute value of the expression Mp. I multiply conjugate of Mp with Mp as

Mp2 = CMp *Mp

which should give me a real expression but it does not give me a real answer and iotas and exponentials are still there. I have tried ComplexExpand and FullSimplify but nothing seems to work properly. If I use ComplexExpand it gives me thousands of terms which ultimately cannot be simplified which is useless expression. What is wrong with my approach and how to correct it? Thank you.

B to Ds simplified.nb (96.8 KB)

2

I have to guess what your question is. I suppose you should learn about ComplexExpand, which is tricky, because it does not use the $Assumptions. A workaround could be this:

FullSimplify[ComplexExpand[ReIm[CMp]]] . {1, I}

Maybe there is a more elegant way, I am curious.

3

Sorry, I see your text only now. Here is a solution:

{reMp, imMp} = Simplify[ComplexExpand[ReIm[Mp]]]
absMp = Sqrt[reMp^2 + imMp^2]

ReIm separates the two parts, so that Simplify does cannot remix them again.

4

It did work. Thanks a lot.