2025 EJC P1 Q8

Do not use a calculator in answering this question.

The complex number \(w\) is such that \(w^2 = 2i\) and \(0 \leq \mathrm{arg}(w) \leq \frac{\pi}{2}\).

1. Find \(w\).[3]
2. Given that one of the roots of the equation \(z^3 - z^2 + (1 - i)z + s = 0\) is \(w\), find the other roots of the equation and the value of \(s\).[5]
3. Hence, find the roots of the equation \(-iv^3 + v^2 + (1 + i)v + s = 0\).[2]