College Algebra, Chapter 1, 1.5, Section 1.5, Problem 64

Find all solutions, real and complex of the equation $\displaystyle x^4 - 16 = 0$


$
\begin{equation}
\begin{aligned}

x^4 - 16 =& 0
&& \text{Given}
\\
\\
(x^4 + x^3) + (x^2 + x) =& 0
&& \text{Group terms}
\\
\\
x^2(x^2 + x) + (x^2 + x) =& 0
&& \text{Factor out } x^2
\\
\\
(x^2 + 1)(x^2 + x) =& 0
&& \text{Factor out } x^2 + 1
\\
\\
x^2 + 1 =& 0 \text{ and } x^2 + x = 0
&& \text{Zero Product Property}
\\
\\
x =& \pm \sqrt{-1} \text{ and } x (x + 1) = 0
&& \text{Solve for } x
\\
\\
x =& \pm \sqrt{i^2} \text{ and } x = 0, x = -1
&& \text{Recall that } i^2 = -1
\\
\\
x =& \pm i \text{ and } x = 0, x = -1
&&


\end{aligned}
\end{equation}
$