$\begingroup$ which oddly enough is true for the majority of analytic elementary functions -- This is true for an analytic function iff it has real coefficients in its Taylor series (as can easily
Solve[a b I/(a + b I) == 4 - 2 I, {a, b},Reals]. Is there a simple way of getting Mathematica to solve this, without knowing lots of special Mathematica commands? In searching out the answer on
Mathematics is a field of study that deals with numbers, shapes, and patterns.
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Simplify [expr ∈ Reals, assum] can be used to try to determine whether an expression corresponds to a real number under the given assumptions. ( x 1 | x 2 | ) ∈ Reals and { x 1 , x 2 } ∈ Reals test whether all x i are real numbers.
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OP asked in Mathematica, it got migrated here. David Richerby said it should be migrated to Computational Science, you say it should be migrated to SO. Meanwhile, I actually answered