# I assume that a parameter is real and positive, but Mathematica still assigns a phase to it

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?

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