Appendix G - Exercises - Page A12: 20

$x=-i$ $x=i$ $x=1$ $x=-1$

Given: $x^{4}=1$ Solve by factoring. $x^{4}-1=0$ As we know, $a^2-b^2=(a+b)(a-b)$, then $(x^{2}-1)(x^{2}+1)=0$ $(x^{2}-(-1))(x+1)(x-1)=0$ $(x+i)(x-i)(x+1)(x-1)=0$ Hence, $x=-i$ $x=i$ $x=1$ $x=-1$