Math Problem Solver

Roots

\[\sqrt{\sqrt{\frac{\frac{44}{5}}{4 B o x}}} = i \left(- \frac{\sqrt[4]{11} \cdot 5^{\frac{3}{4}} \operatorname{im}{\left(\sqrt{\frac{e^{\frac{i \operatorname{atan_{2}}{\left(- \frac{11 \operatorname{im}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)},\frac{11 \operatorname{re}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)} \right)}}{2}}}{\sqrt[4]{\left(\operatorname{re}{\left(B o x\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} \left(\operatorname{im}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{4}}}} \sqrt[8]{\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}}\right)}}{5}\right) - \frac{\sqrt[4]{11} \cdot 5^{\frac{3}{4}} \operatorname{re}{\left(\sqrt{\frac{e^{\frac{i \operatorname{atan_{2}}{\left(- \frac{11 \operatorname{im}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)},\frac{11 \operatorname{re}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)} \right)}}{2}}}{\sqrt[4]{\left(\operatorname{re}{\left(B o x\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} \left(\operatorname{im}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{4}}}} \sqrt[8]{\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}}\right)}}{5} \approx - 1.21788328563091 \operatorname{re}{\left(\sqrt{\frac{e^{\frac{i \operatorname{atan_{2}}{\left(- \frac{11 \operatorname{im}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)},\frac{11 \operatorname{re}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)} \right)}}{2}}}{\sqrt[4]{\left(\operatorname{re}{\left(B o x\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} \left(\operatorname{im}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{4}}}} \sqrt[8]{\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}}\right)} - 1.21788328563091 i \operatorname{im}{\left(\sqrt{\frac{e^{\frac{i \operatorname{atan_{2}}{\left(- \frac{11 \operatorname{im}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)},\frac{11 \operatorname{re}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)} \right)}}{2}}}{\sqrt[4]{\left(\operatorname{re}{\left(B o x\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} \left(\operatorname{im}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{4}}}} \sqrt[8]{\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}}\right)}\]\[\sqrt{\sqrt{\frac{\frac{44}{5}}{4 B o x}}} = i \frac{\sqrt[4]{11} \cdot 5^{\frac{3}{4}} \operatorname{im}{\left(\sqrt{\frac{e^{\frac{i \operatorname{atan_{2}}{\left(- \frac{11 \operatorname{im}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)},\frac{11 \operatorname{re}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)} \right)}}{2}}}{\sqrt[4]{\left(\operatorname{re}{\left(B o x\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} \left(\operatorname{im}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{4}}}} \sqrt[8]{\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}}\right)}}{5} + \frac{\sqrt[4]{11} \cdot 5^{\frac{3}{4}} \operatorname{re}{\left(\sqrt{\frac{e^{\frac{i \operatorname{atan_{2}}{\left(- \frac{11 \operatorname{im}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)},\frac{11 \operatorname{re}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)} \right)}}{2}}}{\sqrt[4]{\left(\operatorname{re}{\left(B o x\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} \left(\operatorname{im}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{4}}}} \sqrt[8]{\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}}\right)}}{5} \approx 1.21788328563091 \operatorname{re}{\left(\sqrt{\frac{e^{\frac{i \operatorname{atan_{2}}{\left(- \frac{11 \operatorname{im}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)},\frac{11 \operatorname{re}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)} \right)}}{2}}}{\sqrt[4]{\left(\operatorname{re}{\left(B o x\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} \left(\operatorname{im}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{4}}}} \sqrt[8]{\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}}\right)} + 1.21788328563091 i \operatorname{im}{\left(\sqrt{\frac{e^{\frac{i \operatorname{atan_{2}}{\left(- \frac{11 \operatorname{im}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)},\frac{11 \operatorname{re}{\left(B o x\right)}}{5 \left(\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}\right)} \right)}}{2}}}{\sqrt[4]{\left(\operatorname{re}{\left(B o x\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(B o x\right)}\right)^{2} \left(\operatorname{im}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{4}}}} \sqrt[8]{\left(\operatorname{re}{\left(B o x\right)}\right)^{2} + \left(\operatorname{im}{\left(B o x\right)}\right)^{2}}\right)}\]