For positive integers n(1), n(2) the val...

For positive integers `n_(1), n_(2)` the value of the expression `(1+i)^(n_(1)) + (1+ i^(3))^(n_(1)) + (1+ i^(5))^(n_(2)) + (1+ i^(7))^(n_(2))`, where `i= sqrt-1` is a real number if and only if

A

A) `n_(1)= n_(2)+1`

B

B) `n_(1)= n_(2)-1`

C

C) `n_(1)=n_(2)`

D

D) `n_(1) gt 0, n_(2) gt 0`

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The correct Answer is:

D

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