# Solution of x^4=1 | Roots of x^4=1

The solutions of x4=1 (x to the power 4 equals 1) are given by x= 1, -1, i, and -i where i=√-1 is the imaginary complex number. In this post, we will learn how to find the roots of x4=1.

## Solutions of x4=1

To solve the given equation x4=1, we need to follow the below steps given here.

Step 1: First, write x4=1 in the form of x4-1=0, then apply the formula of a2-b2.

x4=1

⇒ x4 -1 =0

⇒ (x2)2 -12 =0

⇒ (x2 -1)(x2+1) =0 [applying the formula of a2-b2=(a-b)(a+b) ]

So either x2-1=0 or x2+1=0 …(∗)

Step 2: Now, we will solve the above two equations.

First, solve x2-1=0

⇒ x2-12=0

⇒ (x-1) (x+1)=0

So either x-1=0 or x+1=0

∴ x= 1, -1 …(∗)

Step 3: Now, solve x2+1=0

⇒ x2= -1

⇒ x2= i2

Taking square roots, x= i, -i …(∗∗)

Therefore, from (∗) and (∗∗), we conclude that the solutions of x4=1 are -1, 1, i, and -i where i = √-1.

So there are only two real roots of x^4=1. Ans there are two complex roots of x^4=1.

## Roots of x4=1

Note that the solutions of the equation x4=1 are the same as the roots of x4=1. Thus, from above we deduce that

the roots of x3=1 are ±1 and ±i

where i = √-1 is the imaginary complex number.

How to solve linear equations

Solve x3=1 and find roots

Solve x2+25=0

## FAQs

### Q1: What are the solutions of x4=1?

Answer: The solutions of x^4=1 are x=±1 and ±i where i = √-1 is an imaginary complex number.

### Q2: What are the roots of x4=1?

Answer: The roots of x^4=1 are 1, -1, i, and -i where i=√-1 is the imaginary complex number.

### Q3: Find the number of real roots of x4=1.

Answer: The number of real roots of x^4=1 is two.

### Q4: Find the number of complex roots of x4=1.

Answer: The number of complex roots of x^4=1 is two.