Question

What is the value of n in the equation 0=18+128n^2?

Answer 1

`\large\boxed{\text{no soltion in the set of real numbers}}\\\boxed{n=-(3)/(8)i\ \vee\ n=(3)/(8)i\ \text{in the set of complex numbers}}`

Explanation:

`18+128n^2=0\qquad\text{subtract 18 from both sides}\\\\128n^2=-18\qquad\text{divide both sides by 128}\\\\n^2=-(18)/(128)\\\\n^2=-(18:2)/(128:2)\\\\n^2=-(9)/(64)<0\to\bold{ no\ solution\ in\ the\ set\ of\ real\ numbers}\\\\\bold{In\ the\ set\ of\ Complex\ numbers}\\\\i=√(-1)\\\\n^2=-(9)/(64)\to n=\pm\sqrt{-(9)/(64)}\\\\n=\pm\sqrt{(9)/(64)\cdot(-1)}\\\\n=\pm\sqrt{(9)/(64)}\cdot√(-1)\\\\n=\pm(\sqrt9)/(√(64))i\\\\n=\pm(3)/(8)i`