2703.sagews

a=var('a')
assume(a, 'real')
assume(a>0)
G=1/(a+i);
G_betr=abs(G);
simplify(G_betr)

1/sqrt(a^2 + 1)

Ks = var('Ks')
Kr = var('Kr')
Tn = var('Tn')
w = var('w')
Te = var('Te')

assume(Ks, 'real')
assume(Ks>0)

assume(Kr, 'real')
assume(Kr>0)

assume(Tn, 'real')
assume(Tn>0)

assume(w, 'real')
assume(w>0)

assume(Te, 'real')
assume(Te>0)

#G=(Ks*(Kr+(1/(Tn*i*w))))/((((Ks*(Kr+(1/(Tn*i*w))))/(Te*i*w+1))+1)*(Te*i*w+1))
G=(Ks*(Kr+(1/(Tn*i))))/((((Ks*(Kr+(1/(Tn*i))))/(Te*i+1))+1)*(Te*i+1))
G_betr=abs(G)
G_betr=simplify(G_betr)
G_betr^2 
solve(G_betr==1,Tn)

[Tn == 2*Ks*Te/(2*Kr*Ks + Te^2 + 1)]