\(x^2=-169\\\\in\ the\ real\ numbers\ set\ (\mathbb{R})\ no\ solution\to x\in\O\\\\in\ the\ complex\ _numbers\ set\ (\mathbb{C}):\\\\i=\sqrt{-1}\\\\therefore:\\\\x^2=-169\\\\x=\pm\sqrt{-169}\)
\(x=\pm\sqrt{-1\cdot169}\\\\x=\pm(\sqrt{-1}\cdot\sqrt{169})\\\\x=\pm(i\cdot\sqrt{13^2})\\\\\boxed{x=\pm13i}\)