A real signal g(t) can be represented by a complex basis set.

A set of mutually orthogonal complex signals can never used a basis signal in the Fourier series representation.

Any signal in the time domain can be represented by addition of infinite mutually orthogonal basis signals.

Do the signals 2 cos(2*Pi*f*t) and 3*cos (8*Pi*f*t) are orthogonal?