Solve T=2sqrt{k^2+n^2/gh}

$$T = 2 \sqrt { \frac { k ^ { 2 } + n ^ { 2 } } { g h } }$$

Solve for T (complex solution)

$$T=2\sqrt{\frac{n^{2}+k^{2}}{gh}}$$

$$g\neq 0\text{ and }h\neq 0$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=\frac{4\left(n^{2}+k^{2}\right)}{hT^{2}}\text{, }&h\neq 0\text{ and }k\neq -in\text{ and }k\neq in\text{ and }arg(T)<\pi \text{ and }T\neq 0\\g\neq 0\text{, }&\left(k=in\text{ or }k=-in\right)\text{ and }T=0\text{ and }h\neq 0\end{matrix}\right.$$

Solve for T

$$T=2\sqrt{\frac{n^{2}+k^{2}}{gh}}$$

$$\left(n=0\text{ and }k=0\text{ and }g\neq 0\text{ and }h\neq 0\right)\text{ or }\left(g<0\text{ and }h<0\right)\text{ or }\left(h>0\text{ and }g>0\right)$$

Solve for g

$$\left\{\begin{matrix}g=\frac{4\left(n^{2}+k^{2}\right)}{hT^{2}}\text{, }&\left(n\neq 0\text{ or }k\neq 0\right)\text{ and }h\neq 0\text{ and }T>0\\g\neq 0\text{, }&n=0\text{ and }T=0\text{ and }h\neq 0\text{ and }k=0\end{matrix}\right.$$