Was Metis immortal or did she die when Zeus swallowed her?

Metis was a titan so she was immortal. When Zeus swallowed her she stayed alive in his head, and gave birth to her daughter Athena inside his head. His head was then chopped open and Athena popped out. Some myths say that she stayed inside Zeus' head, and since she was the titan goddess of wisdom she supplied most of Zeus' intelligence.