Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding - Page 112: 74

$x=\pm 2i$ or $x=1$ or $x=-1$

We solve by factoring: $x^{4}+3x^{2}-4=0$ $(x^{2}+4)(x^{2}-1)=0$ $(x^{2}+4)(x-1)(x+1)=0$ $x^{2}+4=0$ or $x-1=0$ or $x+1=0$ $x^2=-4$ or $x=1$ or $x=-1$ $x=\pm\sqrt{-4}$ or $x=1$ or $x=-1$ $x=\pm 2i$ or $x=1$ or $x=-1$