3
$\begingroup$

Very simple question: Why doesn't Mathematica simplify this square root expression?

Refine[Sqrt[Exp[I p]], p > 0] // FullSimplify

It should give

Exp[I p/2] 

Where is my mistake?

$\endgroup$

1 Answer 1

9
$\begingroup$

Just avoid the branch cut:

Refine[Sqrt[Exp[I p]], π > p > 0]

(* ==> E^((I p)/2) *)

The branch cut of the square-root function doesn't allow Mathematica to simplify the expression without the restriction on p from above.

See also the related question and answer here: Using Solve to solve the equation x1/3=−1

$\endgroup$
2
  • 2
    $\begingroup$ As a side note, the simplification is good for Pi > p > -Pi $\endgroup$
    – Bob Hanlon
    Jun 20, 2016 at 16:03
  • $\begingroup$ ...or more precisely, the range of Arg[], from whom Power[] inherits its choice of branch cut. $\endgroup$ Jun 20, 2016 at 17:30

Your Answer

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

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