If I run this line of code

Assuming[{Element[a, Reals], a > 0}, TrigToExp[ComplexExpand[Sqrt[a]]]]

I get

(a^2)^(1/4) E^(1/2 I Arg[a]).

Why does Mathematica assume that the parameter a has a phase, after I declared that it is real and positive?

  • 3
    $\begingroup$ Most Mathematica functions ignore assumptions. TrigToExp appears to be one of those. $\endgroup$ – John Doty Jan 10 '19 at 22:03
  • 2
    $\begingroup$ Could use Refine, as that accounts for assumptions. $\endgroup$ – Daniel Lichtblau Jan 10 '19 at 22:37
  • 1
    $\begingroup$ Simplify[TrigToExp[ComplexExpand[Sqrt[a]]], Assumptions -> {a \[Element] Reals, a > 0}] yields the expected result $\endgroup$ – Mat Jan 11 '19 at 0:03
  • 1
    $\begingroup$ Only functions whose Options include Assumptions make use of $Assumptions or the assumptions specified in Assuming. Neither TrigToExp nor ComplexExpand take the option Assumptions. $\endgroup$ – Bob Hanlon Jan 11 '19 at 2:41

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