Chapter A.7, Problem 57AYU

To determine

To find:The solution of given equation in complex number system.

Answer to Problem 57AYU

The solution of given equation in complex number systemis $3\pm 2i$ .

Explanation of Solution

Given information:

The equationis $x^2-6x+13=0$ .

Calculation:

Consider the equation.

  $\begin{array}{l}{x}^2-6x+13=0\\ x=\frac{-\left(-6\right)\pm \sqrt{{\left(-6\right)}^2-4\left(1\right)\left(13\right)}}{2\left(1\right)}\\ x=\frac{6\pm \sqrt{-16}}{2}\\ x=\frac{6\pm \sqrt{16}\sqrt{-1}}{2}\\ x=\frac{6\pm 4i}{2}\\ x=3\pm 2i\end{array}$