JEE Advanced 2025 Mathematics question
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 = ((-ω.
Then the value of is .
Answer: -2
Solution
, so , a primitive 6th root of unity; any 6 consecutive powers sum to 0. Since 2025 = 6 × 337 + 3, the sum
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