Evaluate i to the power of 4.

'i' also known as 'iota' is defined as the square root of negative 1. It is used to represent a complex number.

Answer: The value of i to the power of 4 is equal to i⁴ = 1.

Let's look into the steps below

Explanation: 

We know that the value of 'i' iota is the square root of negative 1.

It is represented as, i = √-1

Let's take the fourth power on both the sides

⇒ i⁴ = (√-1)⁴

⇒ i⁴ = √-1 × √-1 × √-1 × √-1

⇒ i⁴ = √(-1) × (-1) × (-1) × (-1)

⇒ i⁴ = 1

⇒ i⁴ = 1 

Alternate Approach:

Using Product Law of rules of exponents,

a^m × aⁿ = a^{m + n} 

Thus, i⁴ can be represented as,

i⁴  = i² × i² 

⇒ i⁴  = i² × i²  [Since, i to the power of 2 = -1]

⇒ i⁴  = 1(- 1) × (-1) = 1

Thus, the value of i to the power of 4 is equal to i⁴ = 1.