JEE Advanced 2021 Paper 1 Mathematics Q4

Mathematics

Problem

Let θ1, θ2, …, θ10 be positive valued angles (in radian) such that θ1 + θ2 + ⋯ + θ10 = 2π. Define the complex numbers z1 = e^(iθ1), zk = z(k−1)e^(iθk) for k = 2, 3, …, 10, where i = √−1. Consider the statements P and Q given below: P: |z2 − z1| + |z3 − z2| + ⋯ + |z10 − z9| + |z1 − z10| ≤ 2π Q: |z2² − z1²| + |z3² − z2²| + ⋯ + |z10² − z9²| + |z1² − z10²| ≤ 4π Then,

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