reserve a,b,c,d,a9,b9,c9,d9,y,x1,u,v for Real,
  s,t,h,z,z1,z2,z3,s1,s2,s3 for Complex;

theorem Th25:
  z1<>0 & Polynom(z1,0,z3,z)=0 implies for s st s=-(z3/z1) holds z
= sqrt (( Re s+sqrt ((Re s)^2+(Im s)^2))/2)+ (sqrt ((-Re s+sqrt ((Re s)^2+(Im s
)^2))/2))*<i> or z=-sqrt (( Re s+sqrt ((Re s)^2+(Im s)^2))/2)+ (-sqrt ((-Re s+
sqrt ((Re s)^2+(Im s)^2))/2))*<i> or z= sqrt (( Re s+sqrt ((Re s)^2+(Im s)^2))/
2)+ (-sqrt ((-Re s+sqrt ((Re s)^2+(Im s)^2))/2))*<i> or z=-sqrt (( Re s+sqrt ((
  Re s)^2+(Im s)^2))/2)+ (sqrt ((-Re s+sqrt ((Re s)^2+(Im s)^2))/2))*<i>
proof
  assume z1<>0 & Polynom(z1,0,z3,z)=0;
  then
A1: z^2=(-z3)/z1 by XCMPLX_1:89;
  let s;
  assume s=-(z3/z1);
  hence thesis by A1,Th23;
end;
