look at this pattern
i^2 = -1
i^3 = i^2(i) = -i
i^4= i^2 i^2= (-1)(-1) = +1
i^5 = i
if the exponent is a multiple of 4, the result is +1
so i^37 = (i^36)(i) = i
= (√4√3 i)(√15 i)
= 2√45 i^2
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