Perform the indicated operations and simplify

Question

i^37

sqr-12 x sqr-15

Answer 1

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

(√-12) (√-15)
= (√4√3 i)(√15 i)
= 2√45 i^2
= -6√3