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?
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1 Answer
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2 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– Bob Hanlon2016-06-20 16:03:01 +00:00Commented Jun 20, 2016 at 16:03 - $\begingroup$ ...or more precisely, the range of
Arg[], from whomPower[]inherits its choice of branch cut. $\endgroup$J. M.'s missing motivation– J. M.'s missing motivation2016-06-20 17:30:28 +00:00Commented Jun 20, 2016 at 17:30