Since, |z1|=|z2|=...|z10|=1 θ2=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|≤2π P 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≤4π Q is also true.