Solution
= Solution
Since momentum commutes with the supercharge, part iv gives
$$
[C_{\mu\nu},Q_\alpha]
=[B_\mu,Q_\alpha]P_\nu-[B_\nu,Q_\alpha]P_\mu
=-\frac12(P_\mu P_\nu-P_\nu P_\mu)Q_\alpha=0.
$$
Therefore
$$
\boxed{[C_{\mu\nu},Q_\alpha]=0}.
$$
Hermitian conjugation also gives $[C_{\mu\nu},\bar Q_{\dot\alpha}]=0$.