Solving generating conditional expression despite assumptions

Question

Solve[(-f0 \[Pi]^2 wi^4 + \[Pi]^2 wi^4 z + f0^2 z \[Lambda]^2)/(
   f0 wi Sqrt[((z^2 + (\[Pi]^2 wi^4 (f0 - z)^2)/(
       f0^2 \[Lambda]^2)) \[Lambda]^2)/wi^2]) == 0 && z > 0 && 
  wi > 0 && f0 > 0, z, Reals]

This returns a conditional expression with the same assumptions that I have provided:

{{z -> ConditionalExpression[(
    f0 \[Pi]^2 wi^4)/(\[Pi]^2 wi^4 + f0^2 \[Lambda]^2), 
    wi > 0 && f0 > 0]}}

I know that I can simplify my conditional expression using some assumptions to get rid of this conditional expression wrapper, but this feels inelegant to me because it's not seeing the assumptions that I gave it in Solve[].

How do I get Mathematica to recognize the assumptions I gave it in Solve[]?

Answer 1

The use of a new option Assumptions for Solve does the job:

Solve[(-f0 \[Pi]^2 wi^4 + \[Pi]^2 wi^4 z + 
f0^2 z \[Lambda]^2)/(f0 wi Sqrt[((z^2 + (\[Pi]^2 wi^4 (f0 - 
z)^2)/(f0^2 \[Lambda]^2)) \[Lambda]^2)/wi^2]) == 0 &&
z > 0, z, Reals, Assumptions -> wi > 0 && f0 > 0]

{{z -> (f0 \[Pi]^2 wi^4)/(\[Pi]^2 wi^4 + f0^2 \[Lambda]^2)}}