Answer:
-i
Step-by-step explanation:
The imaginary unit i is defined by the property that [tex]i^2=-1[/tex]. With that in mind, we can list the first few powers of i:
[tex]i^0=1\\i^1=i\\i^2=-1\\i^3=-i\\i^4=1[/tex]
Notice how [tex]i^0[/tex] is the same as [tex]i^4[/tex]? The powers of i are cyclic: they repeat every 4 powers. In general, for any power of i [tex]i^n[/tex]:
[tex]i^n=1[/tex] if [tex]n\div4[/tex] has remainder 0
[tex]i^n=i[/tex] if [tex]n \div 4[/tex] has remainder 1
[tex]i^n=-1[/tex] if [tex]n\div4[/tex] has remainder 2
[tex]i^n=-i[/tex] if [tex]n\div4[/tex] has remainder 3
[tex]35\div4=8R3[/tex], so [tex]i^{35}=-i[/tex]
