If z 1 and z ¯ 1 represents adjacent vertices of a regular polygon of n sides and if I m z 1 R e z 1 = 2 - 1 , then n is equal to

Step-by-step solution

Let z 1 = r e i θ then, z ¯ 1 = r e - i θ z 1 z ¯ 1 = e 2 i θ = e 2 π i / n ⇒   θ = π n Also, I m z 1 R e z 1 = tan θ = tan π n = 2 - 1 ⇒   tan π 8 = 2 - 1 ∴   n = 8