Pensieve Header: Experiments with “Assuming”.

Re[x+I y]

Simplify[Re[(5+4 I) (x+I y)], x∈Reals && y∈Reals]

Expand[(5+4 I) (x+I y)]

Simplify[Re[Expand[(5+4 I) (x+I y)]], x∈Reals && y∈Reals]

Simplify[Re[x+I y], x∈Reals && y∈Reals]

Simplify[Re[(((x+I y))^3)], x∈Reals && y∈Reals]

Refine[Re[(((x+I y))^3)], x∈Reals && y∈Reals]

Simplify[Re[(1/(x+I y))], x∈Reals && y∈Reals]

Refine[Re[(1/(x+I y))], x∈Reals && y∈Reals]

ComplexExpand[(1/(x+I y))]

ComplexExpand[Re[(1/(x+I y))]]

Re[ComplexExpand[(1/(x+I y))]]

ComplexExpand[Im[1/(x+I y)]]

ComplexExpand[Re[(5+4 I) a]]

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