z^2/z^2+2i-0+(1+i)z+i=0 حل کریں

z کے لئے حل کریں

\left\{\begin{matrix}z=\frac{2^{\frac{2}{3}}\left(54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)\right)^{-\frac{1}{3}}\left(\left(54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)\right)^{\frac{2}{3}}-\sqrt[3]{2\left(54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)\right)}+2^{\frac{2}{3}}\left(1-6i\right)\right)}{6}\approx -0.561460888-0.381162591i\text{, }&\sqrt[3]{\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(\frac{25}{54}-\frac{1}{6}i\right)}+\left(\frac{1}{9}-\frac{2}{3}i\right)\left(\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(\frac{25}{54}-\frac{1}{6}i\right)\right)^{-\frac{1}{3}}-\frac{1}{3}\neq -1+i\text{ and }\sqrt[3]{\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(\frac{25}{54}-\frac{1}{6}i\right)}+\left(\frac{1}{9}-\frac{2}{3}i\right)\left(\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(\frac{25}{54}-\frac{1}{6}i\right)\right)^{-\frac{1}{3}}-\frac{1}{3}\neq 1-i\\z=-\frac{2^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)\right)^{-\frac{1}{3}}\left(\sqrt[3]{2}\left(-\sqrt{3}i\sqrt[3]{54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)}+\sqrt[3]{2}\left(2-12i\right)\right)+\left(54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)\right)^{\frac{2}{3}}\left(-\sqrt{3}i-1\right)+\sqrt[3]{2\left(54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)\right)}\right)}{24}\approx -1.353184616+1.12999493i\text{, }&\frac{-1+\sqrt{3}i}{2}\sqrt[3]{\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(\frac{25}{54}-\frac{1}{6}i\right)}+\frac{2\left(\frac{1}{9}-\frac{2}{3}i\right)\left(\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(\frac{25}{54}-\frac{1}{6}i\right)\right)^{-\frac{1}{3}}}{-1+\sqrt{3}i}-\frac{1}{3}\neq -1+i\text{ and }\frac{-1+\sqrt{3}i}{2}\sqrt[3]{\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(\frac{25}{54}-\frac{1}{6}i\right)}+\frac{2\left(\frac{1}{9}-\frac{2}{3}i\right)\left(\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(\frac{25}{54}-\frac{1}{6}i\right)\right)^{-\frac{1}{3}}}{-1+\sqrt{3}i}-\frac{1}{3}\neq 1-i\\z=-\frac{2^{\frac{2}{3}}\left(54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)\right)^{-\frac{1}{3}}\left(-\sqrt{3}i+1\right)\left(\sqrt[3]{2}\left(\sqrt{3}i\sqrt[3]{54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)}+\sqrt[3]{2}\left(2-12i\right)\right)+\left(-1+\sqrt{3}i\right)\left(54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)\right)^{\frac{2}{3}}+\sqrt[3]{2\left(54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)\right)}\right)}{24}\approx 0.914645504-0.748832338i\text{, }&-\frac{\sqrt[3]{2}\left(-1+\sqrt{3}i\right)\left(54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)\right)^{-\frac{1}{3}}\left(-\frac{1}{2}\sqrt{3}\sqrt[3]{2}i\left(54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)\right)^{\frac{2}{3}}-\frac{1}{2}\sqrt{3}\times 2^{\frac{2}{3}}i\sqrt[3]{54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)}+\frac{\sqrt[3]{2}\left(54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)\right)^{\frac{2}{3}}}{2}-\frac{2^{\frac{2}{3}}\sqrt[3]{54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)}}{2}+\left(-2+12i\right)\right)}{12}\neq -1+i\text{ and }-\frac{\sqrt[3]{2}\left(-1+\sqrt{3}i\right)\left(54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)\right)^{-\frac{1}{3}}\left(-\frac{1}{2}\sqrt{3}\sqrt[3]{2}i\left(54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)\right)^{\frac{2}{3}}-\frac{1}{2}\sqrt{3}\times 2^{\frac{2}{3}}i\sqrt[3]{54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)}+\frac{\sqrt[3]{2}\left(54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)\right)^{\frac{2}{3}}}{2}-\frac{2^{\frac{2}{3}}\sqrt[3]{54\sqrt{\frac{1}{3}-\frac{23}{54}i}+\left(25-9i\right)}}{2}+\left(-2+12i\right)\right)}{12}\neq 1-i\end{matrix}\right.