Algebra 2 K. 8 Powers of I EUT Which number equals $$ i^{9} $$ ? W $$ -i \square 1 $$

Question

Algebra 2 > K. 8 Powers of I EUT Which number equals $$ i^{9} $$ ? W $$ -i \square 1 $$

UpStudy AI · Accepted Answer

To determine the value of $$ i^9 $$, let's analyze the powers of the imaginary unit $$ i $$.

The powers of $$ i $$ cycle every four exponents:

$$
\begin{align*}
i^1 &= i \
i^2 &= -1 \
i^3 &= -i \
i^4 &= 1 \
\end{align*}
$$

This cycle repeats every four powers. To find $$ i^9 $$, divide the exponent by 4 and look at the remainder:

$$
9 \div 4 = 2 \text{ with a remainder of } 1
$$

This means:

$$
i^9 = i^{4 \times 2 + 1} = (i^4)^2 \times i^1 = 1^2 \times i = i
$$

**Answer:** $$ i^9 = i $$
$$ i^9 = i $$

Algebra 2 > K. 8 Powers of I EUT
Which number equals ?
W