(i being the complex square root of -1 here.) I have a function which is dependent on the term "y", where, if y is odd, the function is multiplied by i, whereas if y is even the function is multiplied by 1. (y is always a real integer greater than or equal to 0.) How can I add an i^(some y function) term to the function to express this? I have identified that i^(1+multiple of 4)=i, whereas i^(0+multiple of 4)=1. I considered i^(4y-3), but not only does this break down for small values of y, but it yields wrong results for when I want the function to be multiplied by 1 as it never results in a multiple of 4 being the degree of i.