Using symbolic variables, how do you expand polynomials to show complex roots in an equation

Question

bob 2021-9-15

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https://ww2.mathworks.cn/matlabcentral/answers/1454009-using-symbolic-variables-how-do-you-expand-polynomials-to-show-complex-roots-in-an-equation

评论： bob 2021-9-16

This is my code:

clc; clear; close all; 
syms s
Num = 10^4*(s+5)*(s+70);
Den = s*(s+45)*(s+55)*(s^2+7*s+110)*(s^2+6*s+95);
F = Num/Den
h=vpa(partfrac(F,s),5);
pretty(h)

and this is my output:

How do I output it so that that the polynomials are also factored such that:

and also, how do i Output all my roots?

thank you so much in advance

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Answer 1

Robert U 2021-9-16

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https://ww2.mathworks.cn/matlabcentral/answers/1454009-using-symbolic-variables-how-do-you-expand-polynomials-to-show-complex-roots-in-an-equation#answer_788449

在 MATLAB Online 中打开

Hi bob,

I guess it's a transfer function and you are looking for poles and zeros.

syms s

Num = 10^4*(s+5)*(s+70);

Den = s*(s+45)*(s+55)*(s^2+7*s+110)*(s^2+6*s+95);

F = Num/Den;

h=vpa(partfrac(F,s,'FactorMode','complex'),5); % get complex parts of fraction

pretty(h)

0.0066 + 1.0618e-43i 0.0017773 0.13532 - 1.0213 - 0.1349i - 1.0213 + 0.1349i 0.95126 + 0.089607i 0.95126 - 0.089607i -------------------- - --------- + ------- + ------------------ + ------------------ + ------------------- + ------------------- s + 45.0 s + 55.0 s s + 3.0 - 9.2736i s + 3.0 + 9.2736i s + 3.5 - 9.8869i s + 3.5 + 9.8869i

rootsNum = solve(h,s); % calculate actual roots for the rational function

rootsDenum = solve(simplify(1/h),s); % calculate roots for the denumerator

rootsNum

rootsNum =