Answer:
[tex]\large\boxed{\text{no soltion in the set of real numbers}}\\\boxed{n=-\dfrac{3}{8}i\ \vee\ n=\dfrac{3}{8}i\ \text{in the set of complex numbers}}[/tex]
Step-by-step explanation:
[tex]18+128n^2=0\qquad\text{subtract 18 from both sides}\\\\128n^2=-18\qquad\text{divide both sides by 128}\\\\n^2=-\dfrac{18}{128}\\\\n^2=-\dfrac{18:2}{128:2}\\\\n^2=-\dfrac{9}{64}<0\to\bold{ no\ solution\ in\ the\ set\ of\ real\ numbers}\\\\\bold{In\ the\ set\ of\ Complex\ numbers}\\\\i=\sqrt{-1}\\\\n^2=-\dfrac{9}{64}\to n=\pm\sqrt{-\dfrac{9}{64}}\\\\n=\pm\sqrt{\dfrac{9}{64}\cdot(-1)}\\\\n=\pm\sqrt{\dfrac{9}{64}}\cdot\sqrt{-1}\\\\n=\pm\dfrac{\sqrt9}{\sqrt{64}}i\\\\n=\pm\dfrac{3}{8}i[/tex]
