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Given a list, I want to find all elements that have positive imaginary part.

For example, if $y,z\in\mathbb R$ and $a>0$ and the list is $\{ ia+y, -ia+z\}$, then the result should be $\{ia+y\}$.

However, my code using Assuming and Select does not work.

Assuming[{y \[Element] Reals, z \[Element] Reals, a > 0}, 
 Select[{I a + y, -I a + z2}, Im[#] > 0 &]]

Although the expected reslut is {I a + y}, Mathematica gives {}. I suspect that condition given by Assuming seems to be not effective. How can I fix this problem?

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    $\begingroup$ Assuming[{y \[Element] Reals, z2 \[Element] Reals, a > 0}, Select[{I a + y, -I a + z2}, Simplify[Im[#] > 0] &]] $\endgroup$
    – Bob Hanlon
    May 6, 2022 at 2:44

1 Answer 1

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Use Refine to evaluate a > 0

Assuming[{a > 0}, a > 0]
(*a>0*)

Assuming[{a > 0}, Refine[a > 0]]
(*True*)

So you can

Assuming[{y ∈ Reals, z ∈ Reals, a > 0}, Select[{I a + y, -I a + z2}, Refine[Im[#] > 0] &]]

(*{I a + y}*)
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