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I am confused how to assume a variable is pure imaginary. As a test example, I used the code

Assuming[{ x \[Element] I Reals}, Simplify[x + Conjugate[x]]]

In the above, "I" means the imaginary unit. I find that it does not return me 0, but just

x + Conjugate[x]

How shall I let $x$ to be pure imaginary? Many thanks!

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This needs FullSimplify.

FullSimplify[x + Conjugate[x], Re[x] == 0]

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