Final answer:
The posterior cutaneous nerve of the forearm is a branch of the brachial artery and supplies blood to the posterior surface of the arm in the region of the elbow. The deep posterior compartment of the forearm is supplied by the posterior interosseous nerve.
Step-by-step explanation:
The posterior cutaneous nerve of the forearm is a branch of the brachial artery, which is a continuation of the axillary artery in the brachium. It supplies blood to the posterior surface of the arm in the region of the elbow. However, the question seems to be referring to the deep posterior compartment of the forearm, which is supplied by the posterior interosseous nerve (a branch of the radial nerve). This nerve innervates the abductor pollicis longus, extensor pollicis brevis, extensor pollicis longus, extensor indicis, and their associated blood vessels and nerves.