Explanation:

- We need to find the smallest four-digit number that is a perfect square.

- The smallest four-digit number is 1000, and we need its square root to determine the smallest perfect square.

- The square root of 1000 is around 31.62, which is not an integer.

- Checking the square of numbers starting from 32:

- \(32^2 = 1024\)

- 1024 is a four-digit number and a perfect square.

- Option 1, 1024, is the correct and smallest four-digit perfect square.

- Option 2, 1048, Option 3, 1021, and Option 4, 1089 are not perfect squares.

- Therefore, the correct answer is Option 1.