2010013409

Three solutions of the equation $$x^4+8\mathrm{i}=0$$ are $$\begin{array}{r}{x}_1=\sqrt[4]{8}(\cos \frac{3}{8}\pi +\mathrm{i}\sin \frac{3}{8}\pi ),\\ x_2=\sqrt[4]{8}(\cos \frac{7}{8}\pi +\mathrm{i}\sin \frac{7}{8}\pi ),\\ x_3=\sqrt[4]{8}(\cos \frac{15}{8}\pi +\mathrm{i}\sin \frac{15}{8}\pi ).\end{array}$$ Find the fourth solution.