Answer:
C
Step-by-step explanation:
Remember the four basic power of i:
[tex]\begin{aligned}i^1&=i\\i^2&=-1\\i^3&=-i\\i^4&=1\end{aligned}[/tex]
We have:
[tex]i^{233}[/tex]
The trick here is to split the exponent into a number divisible by 4 plus the remainder. Notice that:
[tex]233=232+1[/tex]
And that:
[tex]232/4=58[/tex]
So, we can rewrite our exponent as:
[tex]=i^{4\cdot 58+1[/tex]
Using the properties of exponents:
[tex]=(i^4)^{58}\cdot i^1[/tex]
Since i to the fourth is simply 1:
[tex]=(1)^{58}\cdot i^1[/tex]
Simplify:
[tex]=1\cdot i^1[/tex]
Simplify:
[tex]=i[/tex]
Hence, our answer is C.
