This is an exercise problem from the book "Primes of the form x^2+ny^2: Fermat, Class field Theory and Complex multiplication"
Question: Let $K$ be an imaginary quadratic field, and let $K\subset L$ be a Galois extension. As usual, $\tau$ will denote a complex conjugation. Then if $L$ is Galois over $Q$, then prove that
i) $[L\cap R:Q]=[L:K]$
ii)For $\alpha\in L\cap R$, $L\cap R=Q(\alpha) \Leftrightarrow L=K(\alpha)$
Thanks in advance