[tex]i = \sqrt{-1} \\ i^{2} = -1 \\ i^{3} = -i \\ i^{4} = 1[/tex]
After [tex]i^{4} [/tex], the sequence repeats itself
Divide 37/4 = 9 R 1. Now use the remainder and find which one of the values of i it matches.
[tex]i = i^{1}[/tex] so [tex]i^{37} = i [/tex]
