If $\omega \neq 1$ is a cube root of unity, then what are the solutions of $(z-100)^3 + 1000 = 0$?

What is $(1 + i)^4 + (1 - i)^4$ equal to, where $i=\sqrt{-1}$?

Consider the following statements in respect of a skew-symmetric matrix $A$ of order $3$:

1. All diagonal elements are zero.

2. The sum of all the diagonal elements of the matrix is zero.

3. $A$ is orthogonal matrix.

Which of the statements given above are correct?

Four digit numbers are formed by using the digits 1, 2, 3, 5 without repetition of digits. How many of them are divisible by 4?