How can i find the roots of the complex equation?

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)

Answer 1

[Torsten]

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