Solve y=sqrt{a^2+b^2}

$$y = \sqrt { a ^ { 2 } + b ^ { 2 } }$$

Solve for a (complex solution)

$$a=-\sqrt{y^{2}-b^{2}}$$

$$a=\sqrt{y^{2}-b^{2}}\text{, }arg(y)<\pi \text{ or }y=0$$

Solve for b (complex solution)

$$b=-\sqrt{y^{2}-a^{2}}$$

$$b=\sqrt{y^{2}-a^{2}}\text{, }arg(y)<\pi \text{ or }y=0$$

Solve for a

$$a=\sqrt{y^{2}-b^{2}}$$

$$a=-\sqrt{y^{2}-b^{2}}\text{, }y\geq |b|$$

Solve for b

$$b=\sqrt{y^{2}-a^{2}}$$

$$b=-\sqrt{y^{2}-a^{2}}\text{, }y\geq |a|$$