%exp bases: 
T1 = 1; om1 = 2*pi; delta = 0.005; t = 0:delta:1-delta;  % not quite 1 so that we get precise results. 
eplus = exp(j * om1 *t); eminus = exp(-j * om1 *t); 

%real cosine
x = cos(om1 *t); 
plot3(t,real(eplus),imag(eplus), t,real(eminus),imag(eminus), t,real(x),imag(x)); 
grid; xlabel('t'); ylabel('REAL'); zlabel('IMAG'); 
c1 = 1 / T1 * x * eplus' * delta
cminus1 = 1 / T1 * x * eminus' * delta

%imag cosine
x = j*cos(om1 *t); 
plot3(t,real(eplus),imag(eplus), t,real(eminus),imag(eminus), t,real(x),imag(x)); 
grid; xlabel('t'); ylabel('REAL'); zlabel('IMAG'); 
c1 = 1 / T1 * x * eplus' * delta
cminus1 = 1 / T1 * x * eminus' * delta