Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding - Page 112: 62

$1\pm 2i$

$x^{2}-2x+5=0$ We solve using the quadratic formula ($a=1,\ b=-2,\ c=5$): $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ $x=\frac{-(-2)\pm\sqrt{(-2)^{2}-4(1)(5)}}{2(1)}$ $x=\frac{-(-2)\pm\sqrt{4-20}}{2(1)}$ $x=\frac{+2\pm\sqrt{-16}}{2}$ $x=\frac{2\pm 4i}{2}=1\pm 2i$ Recall, $i=\sqrt{-1}$