Solve 12/a^2+3/b^2=1

$$\frac { 12 } { a ^ { 2 } } + \frac { 3 } { b ^ { 2 } } = 1$$

Solve for a (complex solution)

$$a=-2i\sqrt{3}\left(3-b^{2}\right)^{-\frac{1}{2}}b$$

$$a=2i\sqrt{3}\left(3-b^{2}\right)^{-\frac{1}{2}}b\text{, }b\neq 0\text{ and }b\neq -\sqrt{3}\text{ and }b\neq \sqrt{3}$$

Solve for b (complex solution)

$$b=-\sqrt{3}i\left(12-a^{2}\right)^{-\frac{1}{2}}a$$

$$b=\sqrt{3}i\left(12-a^{2}\right)^{-\frac{1}{2}}a\text{, }a\neq 0\text{ and }a\neq -2\sqrt{3}\text{ and }a\neq 2\sqrt{3}$$

Solve for a

$$a=2\sqrt{-\frac{3}{3-b^{2}}}b$$

$$a=-2\sqrt{-\frac{3}{3-b^{2}}}b\text{, }|b|>\sqrt{3}\text{ and }b\neq 0$$

Solve for b

$$b=\sqrt{-\frac{3}{12-a^{2}}}a$$

$$b=-\sqrt{-\frac{3}{12-a^{2}}}a\text{, }|a|>2\sqrt{3}\text{ and }a\neq 0$$