Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding - Page 112: 59

$3\pm 2i$

$x^{2}-6x+13=0$ We solve using the quadratic formula ($a=1,\ b=-6,\ c=13$): $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ $x=\frac{-(-6)\pm\sqrt{(-6)^{2}-4(1)(13)}}{2(1)}$ $x=\frac{-(-6)\pm\sqrt{36-52}}{2(1)}$ $x=\frac{+6\pm\sqrt{-16}}{2(1)}$ $x=\frac{6\pm 4i}{2}=3\pm 2i$ Recall, $i=\sqrt{-1}$