If i 2 = - 1 and ∑ r = 1 n i r ,   ∀ n ∈ N , is a non-zero real number, then n can be

Step-by-step solution

i p + i p + 1 + i p + 2 + i p + 3 = 0 ,   ∀ p ∈ N So, ∑ r = 1 n i r = 0 for   n = 4 k i       for   n = 4 k + 1 i - 1   for   n = 4 k + 2 - 1   for   n = 4 k + 3   ∀ k ∈ N Hence, n can be 403 for the sum to be non-zero real.