Solve {c}{x^2+y^2=10}{xy=6}

$$\left\{ \begin{array} { c } { x ^ { 2 } + y ^ { 2 } = 10 } \\ { x y = 6 } \end{array} \right.$$

Solve for x, y (complex solution)

$$x=\sqrt{6}e^{\frac{\arctan(\frac{\sqrt{11}}{5})i-2\pi i}{2}}\approx -2.34520788-0.707106781i\text{, }y=\sqrt{6}e^{\frac{-\arctan(\frac{\sqrt{11}}{5})i+2\pi i}{2}}\approx -2.34520788+0.707106781i$$

$$x=\sqrt{6}e^{\frac{\arctan(\frac{\sqrt{11}}{5})i}{2}}\approx 2.34520788+0.707106781i\text{, }y=\sqrt{6}e^{-\frac{\arctan(\frac{\sqrt{11}}{5})i}{2}}\approx 2.34520788-0.707106781i$$

$$x=\sqrt{6}e^{-\frac{\arctan(\frac{\sqrt{11}}{5})i}{2}}\approx 2.34520788-0.707106781i\text{, }y=\sqrt{6}e^{\frac{\arctan(\frac{\sqrt{11}}{5})i}{2}}\approx 2.34520788+0.707106781i$$

$$x=\sqrt{6}e^{\frac{-\arctan(\frac{\sqrt{11}}{5})i-2\pi i}{2}}\approx -2.34520788+0.707106781i\text{, }y=\sqrt{6}e^{\frac{\arctan(\frac{\sqrt{11}}{5})i+2\pi i}{2}}\approx -2.34520788-0.707106781i$$