As Virgil stated, what you want here is Refine
.
Refine[
Sqrt[(γ - κ)^2 - 16*G^2], {κ > 0,
G > 0, γ > 0, (γ - κ)^2 < 16*G^2}]
(* I Sqrt[16 G^2 - (γ - κ)^2] *)
What is the difference between FullSimplify
and Refine
, when they are both given the same Assumptions
? From R.M.'s answer, we learn
The primary difference between Refine
and the two *Simplify
functions is that Refine
only evaluates the expression according
to the assumptions given. It might so happen to be the simplest form
when evaluated, but it does not check to see if it is indeed the
simplest possible form. You should use Refine
when your goal is not
to simplify the expression but to just see how the assumptions
transform it (e.g., square root of a positive quantity).
Simplify
, on the other hand, performs basic algebraic
simplifications and transformations to arrive at the "simplest"
result. Refine
is one among them, and is also mentioned in its doc
page. Here, "simplest" might not necessarily fit your definition of
simple. It is what appears simple to Mathematica, and that is defined
by
LeafCount
.
Refine
rather thanFullSimplify
. $\endgroup$ – Virgil Jan 5 '16 at 4:34