Complex Numbers & Quadratic Equations · JEE Advanced previous year questions

2025 1 question

1. Q132025 · 18 May 2025 · Paper 2· Numerical answer

   For a non-zero complex number $z$, let $\arg (z)$ denote the principal argument of $z$, with $-\pi <\arg (z)\le \pi$. Let $\omega$ be the cube root of unity for which $0<\arg (\omega )<\pi$. Let $$\alpha =\arg \left(\sum _{n=1}^{2025}(-\omega {)}^n\right).$$ Then the value of $\frac{3\alpha }{\pi }$ is ____.

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   Answer: -2