Clear[A, 
      V, EE, k1, k2, m, B1, A2, B2, A3, freal1, freal2, freal3, fim1, fim2, 
      fim3]
A = 1. ;
V = 5. ;
EE = 2.979;
k1 = Sqrt[2*EE];
k2 = Sqrt[2*(EE - V)];
m = {B1, A2, B2, A3} /. 
          Solve[1 + B1 == A2 + B2 && 
              A2*Exp[I*k2*A] + B2*Exp[-I*k2*A] == A3*Exp[I*k1*A] && 
              k1 - k1*B1 == k2*A2 - k2*B2 && 
              A2*k2*Exp[I*k2*A] - B2*k2*Exp[-I*k2*A] == 
                A3*k1*Exp[I*k1*A], {B1, A2, B2, 
              A3}];
{B1, A2, B2, A3} = {m[[1, 1]],  m[[1, 2]], m[[1, 3]],  
        m[[1, 4]]}

freal1 = 
        Re[Exp[I*k1*x] + B1*Exp[-I*k1*x]];
freal2 = 
        Re[A2*Exp[I*k2*x] + 
            B2*Exp[-I*k2*x]];
freal3 = Re[A3*Exp[I*k1*x]];
Plot[freal1, {x, -10, 0}];
Plot[freal2, {x, 0, 1}];
Plot[freal3, {x, 1, 10}];

fim1 = 
        Im[Exp[I*k1*x] + B1*Exp[-I*k1*x]];
fim2 = 
        Im[A2*Exp[I*k2*x] + 
            B2*Exp[-I*k2*x]];
fim3 = Im[A3*Exp[I*k1*x]];
Plot[fim1, {x, -10, 0}];
Plot[fim2, {x, 0, 1}];
Plot[fim3, {x, 1, 10. }];