Question

Simplify.

i^68




1

i

−i

−1

Answer 1

Hello!

In math, i, is also known as the imaginary number. In algebra, we usually use it when a quadratic has an imaginary solution. It can be used when we need to find the negative square root of a number.

Commonly, we know that i × i = -1. Also, there is a unique pattern that occurs.

$i^{0} = 1$

$i^{1}=i$

$i^{2} = -1$

$i^{3} = -i$

This pattern keep repeating forever, including the negative numbers, they show the same pattern.

To solve for $i^{68}$, we can apply the exponent rule, $x^{ab} = (x^{a})^{b}$. Since we know that $i^{2}$ is equal to -1, we can start from there.

$i^{68} =(i^{2})^{34}$

$(-1)^{34} = 1^{34}$ (exponent rule, $(-x)^{n} = x^{n}$)

$1^{34} = 1$

Therefore, the final answer is the first choice, 1.