assuming you mean [tex]i^{77}[/tex] where [tex]i=\sqrt{-1}[/tex]
ok, notice a pattern in the exponent
[tex]i^1=i=\sqrt{-1}[/tex]
[tex]i^2=-1[/tex]
[tex]i^3=-\sqrt{-1}=-i[/tex]
[tex]i^4=1[/tex]
[tex]i^5=i=\sqrt{-1}[/tex]
hum, so it goes 1,2,3,4, then repeats
ok, so every 4, the cycle repeats
how far up is 77 from a multipule of 4?
4*19=76
76 is 1 away from 77
so [tex]i^{77}=(i^{76})(i^1)=[/tex]
[tex](i^4)^{19}(i)=(1)^{19}i=i[/tex]
the answer is B
