Chapter A.7, Problem 65AYU

To determine

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

Answer to Problem 65AYU

The solution of given equation in complex number systemis $-\frac{1}{2}\pm \frac{\sqrt{3}}{2}i$ .

Explanation of Solution

Given information:

The equationis $x^2+x+1$ .

Calculation:

Consider the equation.

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