# JEE-Advanced 2015 (19.C/40)

**Algebra**Level 4

Let \(\omega \neq 1\) be a complex root of unity, find the possible value(s) of \(n\) such that \[(3-3\omega+2\omega^2)^{4n+3}+(2+3\omega-3\omega^2)^{4n+3}+(-3+2\omega+3\omega^2)^{4n+3}=0\] \[\begin{array}{} (1) \, 1 \quad \quad \quad \quad \quad \quad \quad \quad & (2) \, 2 \\ (3) \, 4 & (4) \, 5 \end{array}\] **Note:**

Submit your answer as the increasing order of the serial numbers of all the correct options.

For eg, if your answer is \((1),(2)\), then submit 12 as the correct answer, if your answer is \((2),(3),(4)\), then submit 234 as the correct answer.