The correct answer is option iv. assured.
The synonyms of convinced are persuaded, satisfied, assured, etc.
i. Reluctant means unwilling to do something. So it cannot be the correct one.
ii. In this case, happy is totally a different word. Columbus convinced something, not that he was happy. Happy basically describes mood of a person.
iii. Hesitant goes same with that of reluctant.
Hope it helps
