Math Problem Solver

The solutions are given by the formula: $$x = 4 \cos{\left(\frac{\pi k}{2} \right)} + 4 \sin{\left(\frac{\pi k}{2} \right)} i$$ where $k$ is an integer in $0 \le k < 4$.

There are $2$ real solutions.

There are $2$ solutions with nonzero imaginary part.

Real solutions: $$\begin{aligned}x &= 4\\x &= -4\end{aligned}$$

Solutions with nonzero imaginary part: $$\begin{aligned}x &= 4 i\\x &= -4 i\end{aligned}$$

$i$ is the imaginary unit, defined as $i^2 = -1$.