I want to demonstrate that $(A|v\rangle)^* = \langle v|A^*$
Given only this $(AB)^*=A^*B^*$ and $(|v\rangle, A|w\rangle) = (A^*|v\rangle, |w\rangle)$ Is it possible?
The difficulty is that i don't know how to maniuplate $\langle v|A^*$.
Also: Should I assume that $A|v\rangle = |v_1\rangle$, is $|v_1\rangle^* = \langle v_1|$ or should I also conjugate the vector (and not only take the transposal)?
(I'm reading Nielsen's book: Quantum computation and quantum information)