Question

For positive integers n₁, n₂ the value of expression \((1 + i)^{n_1} + (1 + i^3)^{n_1} + (1 + i^5)^{n_2} + (1 + i^7)^{n_2}\) is a real number if and only if

(a) n₁ = n₂ +1

(b) n₁ = n₂ –1

(c) n₁ = n₂

(d) n₁ > 0, n₂ > 0

Answer 1

(d) n₁ > 0, n₂ > 0