Chapter A.7, Problem 72AYU

To determine

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

Answer to Problem 72AYU

The solution of given equation in complex number system is $\pm 2,\pm i$ .

Explanation of Solution

Given information:

The equationis $x^4+3x^2-4=0$ .

Calculation:

Consider the equation.

  $\begin{array}{l}{x}^4+3x^2-4=0\\ \left(x^2+1\right)\left(x^2-4\right)=0\end{array}$

Equate the factors to zero.

  $\begin{array}{l}{x}^2-4=0\\ x^2=4\\ x=\pm \sqrt{4}\\ x=\pm 2\\ x^2+1=0\\ x=\pm \sqrt{-1}\\ x=\pm i\end{array}$