Résoudre u=log(x^2+y^2)

$$u = \log ( x ^ { 2 } + y ^ { 2 } )$$

Calculer u (solution complexe)

$$u=\log(x^{2}+y^{2})$$

$$x\neq iy\text{ and }x\neq -iy$$

Calculer x (solution complexe)

$$x=-\sqrt{10^{u}-y^{2}}$$

$$x=\sqrt{10^{u}-y^{2}}\text{, }Im(\ln(10^{u}))-\ln(10)Im(u)=0$$

Calculer u

$$u=\log(x^{2}+y^{2})$$

$$y\neq 0\text{ or }x\neq 0$$

Calculer x

$$x=\sqrt{10^{u}-y^{2}}$$

$$x=-\sqrt{10^{u}-y^{2}}\text{, }y\neq 0\text{ and }u\geq \log(y^{2})$$