Simplify i^4k+1, k is subset of counting numbers

i^0 = 1.
i^1 = i.
i^2 = -1.
i^3 = (-1)(i) = -i.
i^4 = (i^2)^2 = (-1)^2 = 1.
i^5 = (i^4)(i) = i.
etc.

2k is an even number, and i to an even power is either -1 or +1.
4k = 2k·2, so i^4k = i^(2k·2) = (i^(2k))^2 = (-1)^2 or (+1)^2, which is +1 in either case.
Therefore i^4k = +1.

i^(4k+1) = (i^4k)(i), which is therefore (+1)(i), or simply i.

above ans is correct.
however
i^ 4= 1 so i^(4k) = 1 => i^(4k+ 1) =i is shorter method


and 4k = 2k·2 is the product of 2k and 2 and not 2k- 2 (there is a dot in the middle and not -)

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