Since, ∣z1∣=∣z2∣=⋯∣z10∣=1θ2=arc(z1z2)∣z2−z1∣= length of line AB≤ length of arcAB∣z3−z2∣= length of line BC≤ length of arcBC∴ Sum of length of these 10 lines ≤ Sum of length of arcs( i.e. 2π)[∵θ1+θ2+θ3+⋯+θ10=2π]∴P:∣z2−z1∣+∣z3−z2∣+⋯+∣z1−z10∣≤2πP is true. Now, ∣z22−z12∣=∣z2−z1∣∣z2+z1∣ We know that ∣z2+z1∣≤∣z2∣+∣z1∣≤2∴∣z22−z1∣2+∣z32−z22∣+⋯+∣z12−z102∣≤2{∣z2−z1∣+∣z2−z2∣+⋯+∣z1−z10∣}≤2(2π)⇒Q≤4πQ is also true.
