Question

Which expression is equivalent i^233? On edge

Answer 1

C

Explanation:

Remember the four basic power of i:

`\begin{aligned}i^1&=i\\i^2&=-1\\i^3&=-i\\i^4&=1\end{aligned}`

We have:

`i^(233)`

The trick here is to split the exponent into a number divisible by 4 plus the remainder. Notice that:

`233=232+1`

And that:

`232/4=58`

So, we can rewrite our exponent as:

`=i^{4\cdot 58+1`

Using the properties of exponents:

`=(i^4)^(58)\cdot i^1`

Since i to the fourth is simply 1:

`=(1)^(58)\cdot i^1`

Simplify:

`=1\cdot i^1`

Simplify:

`=i`

Hence, our answer is C.