Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding - Page 112: 72

$x=1$ or $x=-1$ or $x=\pm i$

We solve by factoring: $x^{4}=1$ $x^{4}-1=0$ $(x^{2}-1)(x^{2}+1)=0$ $(x-1)(x+1)(x^{2}+1)=0$ $x-1=0$ or $x+1=0$ or $x^{2}+1=0$ $x=1$ or $x=-1$ or $x=\pm \sqrt{-1}$ $x=1$ or $x=-1$ or $x=\pm i$ Recall, $i=\sqrt{-1}$