Question

How do you simplify $i^{35}$?

Answer 1

Evaluate the given data using the properties of iota.

We have to evaluate$i^{35}$

$i^{35}$ can be expressed in powers

$$\begin{gathered} \Rightarrow i^{35}=i^{32}.i^2.i \\ \Rightarrow i^{35}={\left(i^4\right)}^8.i^2.i \end{gathered}$$

We know that $i^2=-1$

$$\begin{gathered} \Rightarrow i^4={\left(i^2\right)}^2 \\ \Rightarrow i^4={(-1)}^2 \\ \Rightarrow i^4=1 \end{gathered}$$

Substituting the value in the above equation we get

$$\begin{gathered} \Rightarrow i^{35}={\left(i^4\right)}^8\times i^2\times i \\ \Rightarrow i^{35}=-i \end{gathered}$$

Hence, the required answer is $i^{35}=-i$