It seems like Mathematica cannot separate the expression
x / (z + I*y)
into a pure real and imaginary part with the Re[] and Im[] functions.
What is the correct way to get the separated parts?
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2 Answers
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Use ComplexExpand.
Assuming that x, y and z are all reals:
ComplexExpand[Im[x/(z + I*y)]]
(* -((x y)/(y^2 + z^2)) *)
Assuming that x is complex, the rest are real:
ComplexExpand[Im[x/(z + I*y)], {x}]
(* (z Im[x])/(y^2 + z^2) - (y Re[x])/(y^2 + z^2) *)
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See the documentation for Im:
Im[expr] is left unevaluated if expr is not a numeric quantity.
answered Feb 6, 2017 at 0:39
ComplexExpandto tell Mathematica that variablesx,y, andzare reals. Therefore, to get the imaginary part of theexpr,ComplexExpand[Im[expr]]$\endgroup$