Question

If |ai| < 2, i = 1,2,3, , n and∑aizi = 1 n∈ [i=1,n] then

(1) |z| < 1/3

(2) |z| > 1/3

(3) |z| = 1/3

(4) none of these

Answer 1

Correct option(2) |z|>1/3

Sol.

∑ aizi n∈[i=1,n]= 1

1 = |∑ aizi| n∈[i=1,n]≤ ∑|aizi| n∈[i=1,n]= ∑|ai||zi| n∈[i=1,n]< 2|zi|.