Question

which of the following is equivalent to $i^6$?
a. $-i$
b. $i$
c. $1$
d. $-1$

Explanation:

Step1: Recall the definition of \(i\)

We know that \(i = \sqrt{-1}\), so \(i^2=(\sqrt{-1})^2=- 1\).

Step2: Simplify \(i^6\)

We can rewrite \(i^6\) as \(i^{4 + 2}\). According to the exponent rule \(a^{m + n}=a^m\times a^n\), we have \(i^{4+2}=i^4\times i^2\).
Since \(i^4=(i^2)^2\), and \(i^2 = - 1\), then \((i^2)^2=(-1)^2 = 1\).
We already know that \(i^2=-1\), so \(i^4\times i^2=1\times(-1)=-1\).

Answer:

D. -1