There are three problems.
(1) Mathematica is case-sensitive. You need to replace i with I to get the imaginary unit.
(2) You need to add initial conditions.
(3) The built in methods will not handle complex values. So you will need to split into two sets of variables and equations to represent real and imaginary parts as both being explicitly real.
If you were to replace the complex exponentials by cosines then the variant below will run just fine.
Eqn1 = (1/4)*D[u[x, t], t] - (1 + \[Epsilon]*A*Cos[\[Omega]t])*
D[u[x, t], x] ==
Gr* \[Theta][x, t] + Gc *CC[x, t] +
D[u[x, t], x, x] - (M + 1/B)*u[x, t];
Eqn2 = (1/4)*
D[\[Theta][x, t],
t] - (1 + \[Epsilon]*A*Cos[\[Omega]t]) D[\[Theta][x, t],
x] == (1/Pr) D[\[Theta][x, t], x, x];
Eqn3 = (1/4)*D[CC[x, t], t] - (1 + \[Epsilon]*A*Cos[\[Omega]t])*
D[CC[x, t], x] == (1/Sc) *D[CC[x, t], x, x] - Kr*CC[x, t];
BC1 = u[0, t] == 0;
BC2 = u[inf1, t] == 0;
BC3 = \[Theta][0, t] == 1 + \[Epsilon]*Cos[\[Omega]t];
BC4 = \[Theta][inf1, t] == 0;
BC5 = CC[0, t] == 1;
BC6 = CC[inf1, t] == 0;
ic1 = u[x, 0] == 1;
ic2 = \[Theta][x, 0] == 2.2;
ic3 = CC[x, 0] == x;
inf1 = 5;
param1 = {Gr -> 0.1, Gc -> 0.1, Pr -> 0.71, Sc -> 0.22,
Gc -> 0.1, \[Epsilon] -> 0.001 , M -> 0.1, A -> 0.1, B -> 0.1,
Kr -> 0.1, \[Omega]t -> \[Pi]/4};
Sol1 = NDSolve[{Eqn1, Eqn2, Eqn3, BC1, BC2, BC3, BC4, BC5, BC6} /.
param1, {u, \[Theta], CC}, {t, 0, 8}, {x, 0, 5},
Method -> {"PDEDiscretization" -> {"MethodOfLines",
"SpatialDiscretization" -> {"FiniteElement"}}}]
I realize this alters the problem but it should give an idea of what is needed in order to get the example to run.