Solve {l}{c^{2}=a^{2}+b^{2}}{c^{2}=a^{2}+b^{2}}{a^2+b^2=a^2+b^2}

$$\left. \begin{array} { l } { c ^ { 2 } = a ^ { 2 } + b ^ { 2 } } \\ { c ^ { 2 } = a ^ { 2 } + b ^ { 2 } } \\ { a ^ { 2 } + b ^ { 2 } = a ^ { 2 } + b ^ { 2 } } \end{array} \right.$$

Solve for c, a, b (complex solution)

$$c=\sqrt{a^{2}+b^{2}}\text{, }a\in \mathrm{C}\text{, }b\in \mathrm{C}$$

$$c=-\sqrt{a^{2}+b^{2}}\text{, }a\in \mathrm{C}\text{, }b\in \mathrm{C}$$

Solve for c, a, b

$$c=-\sqrt{a^{2}+b^{2}}\text{, }a\in \mathrm{R}\text{, }b\in \mathrm{R}$$

$$c=\sqrt{a^{2}+b^{2}}\text{, }a\in \mathrm{R}\text{, }b\in \mathrm{R}$$