Solve (c=1/sqrt{epsilon_{0}mu_{0}}

$$( c = 1 / \sqrt { \epsilon _ { 0 } \mu _ { 0 } }$$

Solve for c (complex solution)

$$c=\left(\mu _{0}ϵ_{0}\right)^{-\frac{1}{2}}$$

$$\mu _{0}\neq 0\text{ and }ϵ_{0}\neq 0$$

Solve for μ_0 (complex solution)

$$\mu _{0}=\frac{1}{ϵ_{0}c^{2}}$$

$$c\neq 0\text{ and }ϵ_{0}\neq 0\text{ and }arg(\sqrt{\frac{1}{c^{2}}}c)<\pi$$

Solve for c

$$c=\frac{1}{\sqrt{\mu _{0}ϵ_{0}}}$$

$$\left(ϵ_{0}<0\text{ and }\mu _{0}<0\right)\text{ or }\left(\mu _{0}>0\text{ and }ϵ_{0}>0\right)$$

Solve for μ_0

$$\mu _{0}=\frac{1}{ϵ_{0}c^{2}}$$

$$c>0\text{ and }ϵ_{0}\neq 0$$