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?


1 Answer 1


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

  • 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

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