Multiple choice

The roots of the equation $x^4-1=0$, are?

  1. $1, 1, i, -i$
  2. $1, -1, i, -i$
  3. $1, -1, \omega, \omega^2$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

x^4 - 1 = 0 => (x^2 - 1)(x^2 + 1) = 0. (x-1)(x+1)(x-i)(x+i) = 0. Roots are 1, -1, i, -i.

AI explanation

To find the roots of the equation, we set the polynomial to zero by writing x^4 - 1 = 0. Using the algebraic identity for the difference of squares, we factor it as (x^2 - 1)(x^2 + 1) = 0. This gives x^2 = 1, which yields 1 and -1, and x^2 = -1, which yields i and -i. The roots are 1, -1, i, and -i.

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