Question

simplify: j to the 107 power

Answer 1

is j defined as
\[ j = \sqrt{-1} \]?

Answer 2

As you hinted phi, I think he missed the i, it's just next to the j in the keyboard.
If its i to the 107 power, we need to know that i to the 4 power is 1, so I to the 107 power can be decompossed as (i^4)^26*i^3 (we divide the power, 107, by 4 and place the residue outside the parenthesis and the result outside, so:)
i^k=(i^4)^(entire part of k div 4)*i^(residue k div 4).
Finally, as i^4 is equal to 1, and 1^26=1, we have i^107=i^3, which is equal to i^2*i=(-1)*i