Question 57252
You only have 1 of 2 possiblities: 1 or -1.  That's because {{{i^2=-1}}}.  Note that {{{i^55}}} can be rewritten as {{{i*i^54}}}.  Also note that {{{i^54}}} can be rewritten as {{{i^2}}} 27 times; that means that {{{i^54=-1}}} because {{{i^2*i^2=1}}}.  So we now have {{{i^55=i*i^54=i*(-1)=-i}}}, or {{{i^55=-i}}}.