I am read a solution (4.9) Here say:
... both $a, d$ are pure phases, so that it is always possible to find (non unique) real numbers $\alpha, \beta, \delta$ such that $a = e^{i(\alpha−\beta/2−\delta/2)}$...
My question: What is a pure phases? Why $a, d$ are pure phase?. Why it is always possible to find (non unique) real numbers $\alpha, \beta, \delta$ such that $a = e^{i(\alpha−\beta/2−\delta/2)}$?
...Therefore it is possible to assume that none of the cœfficients $a, b, c, d$ vanish. In particular, there are real numbers $0 < γ, γ^{'} < \pi$ such that $|a| = \cos γ/2$
Why the module of any Complex number can be represented than $\sin$ or $\cos$ functions?