Hit "Shift Return" whith the cursor in each line, to make it evaluate the line. (Or use "Evaluate Notebook" in the Evaluation menu to do them all at once)
Syntax matters - watch for square brackets vs curly brackets vs parentheses, capitals, colons, etc.

Here is a simple example of the use of complex values. Look up Conjugate if you cannot figure out what it should do.

f[a_]:=Exp[-I*a*Pi]

f[1/2]

Conjugate[f[1/2]]

Conjugate[f[1/2]]*f[1/2]

(Abs[(2*Exp[-I*Pi] + 4*Exp[-2 *I*Pi])])^2

Now how about working with some complex wave functions? This is where it can take a bit of massaging to get Mathematica to write things down in a familiar way. Look up functions like ComplexExpand and Simplify.

Psin[n_Integer,x_]:=Sqrt[2/a]*Sin[n*Pi*x/a]*Exp[-I*n^2*ω*t]

Psinm[n_Integer,m_Integer,x_]:=(1/Sqrt[2])*(Psin[n,x,ω]+Psin[m,x,ω])

Psinm[1,2,x]

Here is where it gets messy. Notice the asterisk for complex conjugate instead of the more clunky Conjugate function. It is available through one of the many Mathematica keyboard shortcuts (Esc/conj/Esc where Esc means hit the escape key).

Simplify[ComplexExpand[Psinm[1,2,x]\[Conjugate]Psinm[1,2,x]]]

Manipulate[Plot[Re[Psinm[1,2,x,1,1]/.{t->u,a->1,ω->1}],{x,0,1},PlotRange->{-1.8,1.8}],{u,0,2*Pi}]