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}=

Explanation:

Step1: Rewrite the exponent

Express $i^{37}$ as $i^{36 + 1}=i^{36}\times i^{1}$.

Step2: Rewrite $i^{36}$

Since $i^{4}=1$, and $36\div4 = 9$, we can write $i^{36}=(i^{4})^{9}$.

Step3: Calculate $(i^{4})^{9}$

$(i^{4})^{9}=1^{9}=1$.

Step4: Find the value of $i^{37}$

$i^{37}=i^{36}\times i^{1}=1\times i = i$.

Answer:

$i$