so I understand a little of branch cuts, but clearly not enough....

can someone please explain to me why Mathematica doesn't simplify the following expression given that the denominator is explicitly Real (and positive after squaring)

In[560]:= FullSimplify[1/Sqrt[(y z + Conjugate[y] Conjugate[z])^2] ]

Out[560]= 1/Sqrt[(y z + Conjugate[y] Conjugate[z])^2]

Probably a simple one, I know, but I really don't get it. A naive use of ComplexExpand doesn't get me anywhere either.

Is it because Mathematica thinks that 1/Abs[y z + Conjugate[y] Conjugate[z]] is more complicated?

Thanks in advance


1 Answer 1

expr1 = 1/Sqrt[(y z + Conjugate[y] Conjugate[z])^2];

expr2 = ComplexExpand[
   expr1 /. {y -> a + b*I, z -> c + d*I},
   TargetFunctions -> {Re, Im}] // FullSimplify

(*  1/(2*((a*c - b*d)^4)^(1/4))  *)

expr3 = expr2 /.
  {a -> Re[y], b -> Im[y], c -> Re[z], d -> Im[z]}

(*  1/(2*(((-Im[y])*Im[z] + Re[y]*Re[z])^4)^(1/4))  *)

expr1 == expr3 // FullSimplify

(*  True  *)

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.