Let \theta_{1}, \theta_{2}, . . ., \theta_{10} be positive valued angles (in radian) such that \theta_{1}+\theta_{2}+. . .+\theta_{10}=2 \pi. Define the complex numbers z_{1}=e^{i \theta 1}, z_{ {k}}=z_{k-1} e^{i \theta_{k}} for k=2,3, . . ., 10, where i=\sqrt{-1}. Consider the statements P and Q given below : Pz_{2}-z_{1}|+z_{3}-z_{2}|+. . .+z_{10}-z_{9}|+z_{1}-z_{10}| \leq 2 \pi Qz_{2}^{2}-z_{1}^{2}|+z_{3}^{2}-z_{2}^{2}|+. . .+z_{10}^{2}-z_{9}^{2}|+z_{1}^{2}-z_{10}^{2}| \leq 4 \pi [JEE Adv 2021 P1]

Correct Answer is : both P and Q are TRUE

Complex Numbers

Section: Mathematics

Question : 11 of 36

Marks: +1, -0

Let θ1,θ2,...,θ10 be positive valued angles (in radian) such that θ1+θ2+...+θ10=2π. Define the complex numbers z1=eiθ1,zk=zk−1eiθk for k=2,3,...,10, where i=√−1. Consider the statements P and Q given below : Pz2−z1|+z3−z2|+...+z10−z9|+z1−z10|≤2π Qz22−z12|+z32−z22|+...+z102−z92|+z12−z102|≤4π

[JEE Adv 2021 P1]

P is TRUE and Q is FALSE
Q is TRUE and P is FALSE
both P and Q are TRUE
both P and Q are FALSE

Validate

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