# Meaning of phase relationship for a superposition of states

I have studied an introductory course in quantum mechanics, and yet I still do not understand the significance of a phase difference between quantum states that a system is in a superposition of. In my lecture notes, it is stated that

Form a linear combination of two quantum states:

$|\psi \rangle = c_1|\phi_1\rangle + c_2|\phi_2\rangle$

$|\psi \rangle = e^{i\theta_1}|\phi_1\rangle + e^{i\theta_2}|\phi_2\rangle$

$|\psi \rangle = e^{i\theta_1}(|\phi_1\rangle + e^{i(\theta_2-\theta_!)}|\phi_2\rangle)$

The resultant vector, and therefore the outcome of any experiemt, depends on the relative quantum phase difference between the two states

This has me confused on many levels. Aside from the fact that the state is simple not normalised here (we would require a factor of $\frac{1}{\sqrt2}$ at the front), the magnitudes of each of the coefficients are equal, unless we allow $\theta$ to be complex which I do not think is intended here.