Whakaoti i te z=sqrt{x^4+y^4}

$$z = \sqrt { x ^ { 4 } + y ^ { 4 } }$$

Whakaoti mō x (complex solution)

$$x=i\sqrt[4]{z^{2}-y^{4}}$$

$$x=\sqrt[4]{z^{2}-y^{4}}$$

$$x=-\sqrt[4]{z^{2}-y^{4}}$$

$$x=-i\sqrt[4]{z^{2}-y^{4}}\text{, }arg(z)<\pi \text{ or }z=0$$

Whakaoti mō y (complex solution)

$$y=i\sqrt[4]{z^{2}-x^{4}}$$

$$y=\sqrt[4]{z^{2}-x^{4}}$$

$$y=-\sqrt[4]{z^{2}-x^{4}}$$

$$y=-i\sqrt[4]{z^{2}-x^{4}}\text{, }arg(z)<\pi \text{ or }z=0$$

Whakaoti mō x

$$x=\sqrt[4]{z^{2}-y^{4}}$$

$$x=-\sqrt[4]{z^{2}-y^{4}}\text{, }z\geq y^{2}$$

Whakaoti mō y

$$y=\sqrt[4]{z^{2}-x^{4}}$$

$$y=-\sqrt[4]{z^{2}-x^{4}}\text{, }z\geq x^{2}$$