Question

If $n₁, n₂$ are positive integers, then $(1+i)ⁿ₁+(1+i³)ⁿ₁+(1+i⁵)ⁿ₂+(1+i⁷)ⁿ₂$ is a real number if and only if

• A. $n_1 = n_2 + 1$
• B. $n_1 = n_2$
• C. $n_1, n_2$ are any two negative integers
• D. $n_1, n_2$ are both any positive integers

Hint:

If $n1, n2$ are positive integers, then $(1+i)+(1+i)+(1+i)$ is a real number if and only if

Answer 1

The Correct Option is D