How can i find the roots of the complex equation?

Question

Sahil Wani 2023-6-19

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https://ww2.mathworks.cn/matlabcentral/answers/1985169-how-can-i-find-the-roots-of-the-complex-equation

编辑： Torsten 2023-6-19

I need to find the root of the following equation in matlab. Can can anyone help me to find the z values.

root(z^8 + (10548593400*z^6)/42679 + (33343133111071335000*z^4)/1821497041 + (211014867341025000000*z^2)/554827 - 142793543857500000000000000/10778089, z, 1)

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Answer 1

Torsten 2023-6-19

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https://ww2.mathworks.cn/matlabcentral/answers/1985169-how-can-i-find-the-roots-of-the-complex-equation#answer_1258694

编辑：Torsten 2023-6-19

在 MATLAB Online 中打开

You can get an analytical solution if you substitute y = z^2:

syms y
p = y^4 + (10548593400*y^3)/42679 + (33343133111071335000*y^2)/1821497041 + (211014867341025000000*y)/554827 - 142793543857500000000000000/10778089;
ysol = solve(p,y,'MaxDegree',4);
zsol = [sqrt(ysol),-sqrt(ysol)];
double(zsol)
ans = 
   1.0e+02 *

   0.0000 + 3.7607i   0.0000 - 3.7607i
   1.3098 + 0.0000i  -1.3098 + 0.0000i
   0.7889 - 2.6013i  -0.7889 + 2.6013i
   0.7889 + 2.6013i  -0.7889 - 2.6013i
syms z
sol = roots(sym2poly(z^8 + (10548593400*z^6)/42679 + (33343133111071335000*z^4)/1821497041 + (211014867341025000000*z^2)/554827 - 142793543857500000000000000/10778089))
sol = 
   1.0e+02 *

   0.0000 + 3.7607i
   0.0000 - 3.7607i
   0.7889 + 2.6013i
   0.7889 - 2.6013i
  -0.7889 + 2.6013i
  -0.7889 - 2.6013i
  -1.3098 + 0.0000i
   1.3098 + 0.0000i