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Question: The roots of the equation\(x^{4} - 1 = 0\), are...

The roots of the equationx4−1=0x^{4} - 1 = 0, are

A

1,1,i,−i1,1,i, - i

B

1,−1,i,−i1, - 1,i, - i

C

1,−1,ω,ω2\mathbf{1,}\mathbf{-}\mathbf{1,\omega,}\mathbf{\omega}^{\mathbf{2}}

D

None

Answer

1,−1,i,−i1, - 1,i, - i

Explanation

Solution

Sol. Given equation x4−1=0⇒(x2−1)(x2+1)=0\mathbf{x}^{\mathbf{4}}\mathbf{-}\mathbf{1 = 0}\mathbf{\Rightarrow}\mathbf{(}\mathbf{x}^{\mathbf{2}}\mathbf{-}\mathbf{1)(}\mathbf{x}^{\mathbf{2}}\mathbf{+ 1) = 0}

⇒x2=1\mathbf{\Rightarrow}\mathbf{x}^{\mathbf{2}}\mathbf{= 1} and x2=−1x^{2} = - 1

⇒ x=±1,±ix = \pm 1, \pm i