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