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I'm new to wolfram and I was solving an optimization question in wolfram. For that I need to calculate the objective function.

From my calculations I got a equation (with complex numbers) as follows:

0.` + 3.35`/((23.4256` + (0.` + 3.35`/\[Alpha])^2) \[Alpha]) + 
 I (-(4.84`/(23.4256` + (0.` + 3.35`/\[Alpha])^2)) + (
    3 \[Pi] \[Alpha]^2)/500 - 108.`/(
    11664.` + 3.0976`/(\[Alpha] - \[Beta])^2)) + 1.76`/((11664.` + 
    3.0976`/(\[Alpha] - \[Beta])^2) (\[Alpha] - \[Beta]))

eqn

Now I need to collect the real part from the above equation which is easy, but after that I need to equate the real part to zero and rearrange it in the following form

$$A_5 \alpha^5 + A_4 \alpha^4 + A_3 \alpha^3 + A_2 \alpha^2 + A_1 \alpha + A_0 = 0$$

What should I do ? Assuming $\alpha $ and $\beta$ are real numbers.

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This should work:

Collect[Numerator@Together@ComplexExpand@Re@expr, α] == 0
(* 0.143157 α^3 - 0.0000722876 β - 0.286163 α^2 β + 0.143157 α (0.000770244 + 0.998946 β^2) == 0 *)

where expr is your expression. What this does:

  • Re: Get the real part of expr
  • ComplexExpand: Simplify, assuming all variables are real. This gets rid of the explicit Re/Im
  • Together: Write everything onto one fraction
  • Numerator: Take the numerator of said fraction. This is equivalent to multiplying both sides of the equations with the denominator: $\frac ab=0\Rightarrow a=b\cdot 0\Rightarrow a=0$
  • Collect: Write the result as a sum of powers of α
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