What is i^51 + i^399?

-i - i
0

i^0 = 1 by definition of "power 0"
i^1 = i
i^2 = -1 by definition of i *
i^3 = -i because i^3 = i*i^2 = i(-1)
i^4 = +1 because i^4 = (i^2)^2 = (-1)^2 = 1 = i^0
and the cycle repeats itself.

i^n ?
Divide n by 4
keep only the remainder
look it up on the cycle list.

i^51 is the same as i^3
because i^51 = (i^48)(i^3) = 1(i^3) = -i

i^399 is the same as i^3
i^399 = (i^396)(i^3) = 1(i^3) = -i

sum = -2i

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* in maths, it is i^2 which is defined, not i.

i = -1^1/2 = -1^0.5

The answer is i^450

I love how all of the answers are different.

-2 , any i to a even power is + and odd power is - . So -1 + -1 is -2