Our teacher told us that basic arithmetic is essential to our day-to-day activities.

The word essential means absolutely necessary or important. D. necessary is the best synonym for essential. The answer is $\boxed{\text{D}}$

The word complex means consisting of many different and connected parts, often making it difficult to understand or solve. C. difficult is the best synonym for complex in this context. The answer is $\boxed{\text{C}}$

The word vices refers to immoral or wicked behavior, or bad habits. A. weaknesses (especially moral weaknesses or character flaws) is the best synonym for vices. The answer is $\boxed{\text{A}}$