# Simplifying square root of exponential

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?

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.

• As a side note, the simplification is good for Pi > p > -Pi – Bob Hanlon Jun 20 '16 at 16:03
• ...or more precisely, the range of Arg[], from whom Power[] inherits its choice of branch cut. – J. M. will be back soon Jun 20 '16 at 17:30