# 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 i^{4} = 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

⇒ i^{4} = (√-1)^{4}

⇒ i^{4} = √-1 × √-1 × √-1 × √-1

⇒ i^{4} = √(-1) × (-1) × (-1) × (-1)

⇒ i^{4} = 1

⇒ i^{4} = 1

Alternate Approach:

Using Product Law of rules of exponents,

a^{m} × a^{n} = a^{m + n}

Thus, i^{4} can be represented as,

i^{4} = i^{2} × i^{2}

⇒ i^{4} = i^{2} × i^{2} [Since, i to the power of 2 = -1]

⇒ i^{4} = 1(- 1) × (-1) = 1

### Thus, the value of i to the power of 4 is equal to i^{4} = 1.

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