Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding - Page 112: 60

$-2\pm 2i$

$x^{2}+4x+8=0$ We solve using the quadratic formula ($a=1,\ b=4,\ c=8$): $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ $x=\frac{-4\pm\sqrt{4^{2}-4(1)(8)}}{2(1)}$ $x=\frac{-4\pm\sqrt{16-32}}{2(1)}$ $x=\frac{-4\pm\sqrt{-16}}{2(1)}$ $x=\frac{-4\pm 4i}{2}=-2\pm 2i$ Recall, $i=\sqrt{-1}$