Question

Let α_r = e^{i2π r/n} (1 ≤ r ≤ n) be the complex number associated with the point Ar on Argand plane, and point B is (2, 0). Then the value of BA₁ ⋅ BA₂ ⋅ BA₃ … BA_n is equal to

(A)  n

(B)  2^{n − 1} 

(C)  2n

(D)  2n - 1

Answer 1

Correct option   (C)  π

xⁿ − 1 = (x − α₁) (x − α₂) (x − α₃) … (x − α_n)

By Putting x = 2,

2^{n − 1} = (2 − α₁) (2 − α₂) … (2 − α_n–1)

⇒ |2 − α₁| |2 − α₂| … |2 − α_n−1| = |2ⁿ − 1| = 2ⁿ − 1