Start with second, third and fourth degree of imaginary unit i:
[tex]i^2=-1, \\ i^3=i^2\cdot i=-1\cdot i=-i, \\ i^4=i^2\cdot i^2=-1\cdot (-1)=1[/tex].
Since 233=232+1=4·58+1, then [tex]i^{233}=i^{4\cdot 58+1}=(i^4)^{58}\cdot i^1=1^{58}\cdot i=i[/tex].
Answer: [tex]i^{233}=i[/tex]
