Solve varepsilon=sqrt{sigma^2/n}

$$\varepsilon = \sqrt { \frac { \sigma ^ { 2 } } { n } }$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=\left(\frac{\sigma }{\epsilon }\right)^{2}\text{, }&\sigma \neq 0\text{ and }arg(\epsilon )<\pi \text{ and }\epsilon \neq 0\\n\neq 0\text{, }&\epsilon =0\text{ and }\sigma =0\end{matrix}\right.$$

Solve for ε (complex solution)

$$\epsilon =\sqrt{\frac{\sigma ^{2}}{n}}$$

$$n\neq 0$$

Solve for n

$$\left\{\begin{matrix}n=\left(\frac{\sigma }{\epsilon }\right)^{2}\text{, }&\sigma \neq 0\text{ and }\epsilon >0\\n\neq 0\text{, }&\sigma =0\text{ and }\epsilon =0\end{matrix}\right.$$

Solve for ε

$$\epsilon =\sqrt{\frac{\sigma ^{2}}{n}}$$

$$\left(\sigma =0\text{ and }n\neq 0\right)\text{ or }n>0$$