Question

$i^{23} = i^{20+3}$
$= i^{20} \times i^{3}$
$= (i^{4})^{5} \times i^{3}$
$= 1^{5} \times i^{3}$
$= 1 \times i^{3}$
$= -i$
use the example as a model. simplify the expressions.
$i^{37} = $
options:
$i$
$-i$
$1$
$-1$

Explanation:

Step1: Split exponent into sum

$i^{37}=i^{36+1}$

Step2: Rewrite as product of powers

$=i^{36} \times i^{1}$

Step3: Express as power of $i^4$

$=(i^4)^9 \times i$

Step4: Substitute $i^4=1$

$=1^9 \times i$

Step5: Simplify $1^9$

$=1 \times i$

Step6: Final simplification

$=i$

Answer:

$i$