Question

Simplify

$i^{14}$

Short answer

The simplified value of expression is $i^{14}=-1$.

Step-by-step solution

Step 1. Given Information.

Given to simplify the expression $i^{14}$

Step 2. Explanation.

From the properties of complex numbers, $i^2=-1$

Using the above property,

$\begin{array}{l}{i}^{14}=i^{2\times 7}\\ i^{14}={\left(i^2\right)}^7\\ i^{14}={\left(-1\right)}^7\\ i^{14}=-1\end{array}$

Step 3. Conclusion.

Therefore, the simplified value of expression is $i^{14}=-1$.