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 (\sum_{n=1}^{2025}(-\omega)^n) Then the value of \frac{3 \alpha}{\pi} is \_\_\_\_ . [JEE Adv 2025 P2]

Complex Numbers

Section: Mathematics

Question : 1 of 36

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For a non-zero complex number z, let arg(z) denote the principal argument of z, with −π<arg(z)≤π.
Let ω be the cube root of unity for which 0<arg(ω)<π.
Let α=arg(

2025

∑

n=1

(−ω)n)
Then the value of ‌

3α

is ____ .

[JEE Adv 2025 P2]

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