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

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

Answer 1

[Robert U]

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 = 

rootsDenum

rootsDenum = 

Kind regards,

Robert

[bob]

Thank you so much!