For a non-zero complex number $z$, let $\arg (z)$ denote the principal argument of $z$, with $-\pi

Question

For a non-zero complex number $z$, let $\arg (z)$ denote the principal argument of $z$, with $-\pi<\arg (z) \leq \pi$. 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_________. [JEE Advanced 2025]

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For a non-zero complex number \(z\), let \(\arg (z)\) denote the principal argument of \(z\), with \(-\pi<\arg (z) \l…

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For a non-zero complex number \(z\), let \(\arg (z)\) denote the principal argument of \(z\), with \(-\pi&lt;\arg (z) \l…

Practice more JEE Maths PYQs

For a non-zero complex number \(z\), let \(\arg (z)\) denote the principal argument of \(z\), with \(-\pi<\arg (z) \l…