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]))
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.