Simplifying square root of exponential

Question

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?

score 9 · Answer 1 · edited Apr 13 '17 at 12:55

9

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

edited Apr 13 '17 at 12:55

Community

answered Jun 20 '16 at 15:55

Jens

2

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.'s missing motivation Jun 20 '16 at 17:30

1 Answers1