Math Problem Solver

Roots

\[\sqrt{39 \cdot {y}^{9}} = i \sqrt[4]{\left(351 \left(\operatorname{re}{\left(y\right)}\right)^{8} \operatorname{im}{\left(y\right)} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{6} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{4} \left(\operatorname{im}{\left(y\right)}\right)^{5} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{7} + 39 \left(\operatorname{im}{\left(y\right)}\right)^{9}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{9} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{7} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{5} \left(\operatorname{im}{\left(y\right)}\right)^{4} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{3} \left(\operatorname{im}{\left(y\right)}\right)^{6} + 351 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{8}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(351 \left(\operatorname{re}{\left(y\right)}\right)^{8} \operatorname{im}{\left(y\right)} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{6} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{4} \left(\operatorname{im}{\left(y\right)}\right)^{5} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{7} + 39 \left(\operatorname{im}{\left(y\right)}\right)^{9},39 \left(\operatorname{re}{\left(y\right)}\right)^{9} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{7} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{5} \left(\operatorname{im}{\left(y\right)}\right)^{4} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{3} \left(\operatorname{im}{\left(y\right)}\right)^{6} + 351 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{8} \right)}}{2} \right)} + \sqrt[4]{\left(351 \left(\operatorname{re}{\left(y\right)}\right)^{8} \operatorname{im}{\left(y\right)} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{6} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{4} \left(\operatorname{im}{\left(y\right)}\right)^{5} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{7} + 39 \left(\operatorname{im}{\left(y\right)}\right)^{9}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{9} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{7} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{5} \left(\operatorname{im}{\left(y\right)}\right)^{4} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{3} \left(\operatorname{im}{\left(y\right)}\right)^{6} + 351 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{8}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(351 \left(\operatorname{re}{\left(y\right)}\right)^{8} \operatorname{im}{\left(y\right)} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{6} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{4} \left(\operatorname{im}{\left(y\right)}\right)^{5} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{7} + 39 \left(\operatorname{im}{\left(y\right)}\right)^{9},39 \left(\operatorname{re}{\left(y\right)}\right)^{9} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{7} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{5} \left(\operatorname{im}{\left(y\right)}\right)^{4} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{3} \left(\operatorname{im}{\left(y\right)}\right)^{6} + 351 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{8} \right)}}{2} \right)} \approx 70.0999286732875 i \left(\left(0.0714285714285714 \left(\operatorname{re}{\left(y\right)}\right)^{8} \operatorname{im}{\left(y\right)} - 0.666666666666667 \left(\operatorname{re}{\left(y\right)}\right)^{6} \left(\operatorname{im}{\left(y\right)}\right)^{3} + \left(\operatorname{re}{\left(y\right)}\right)^{4} \left(\operatorname{im}{\left(y\right)}\right)^{5} - 0.285714285714286 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{7} + 0.00793650793650794 \left(\operatorname{im}{\left(y\right)}\right)^{9}\right)^{2} + \left(0.00793650793650794 \left(\operatorname{re}{\left(y\right)}\right)^{9} - 0.285714285714286 \left(\operatorname{re}{\left(y\right)}\right)^{7} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{5} \left(\operatorname{im}{\left(y\right)}\right)^{4} - 0.666666666666667 \left(\operatorname{re}{\left(y\right)}\right)^{3} \left(\operatorname{im}{\left(y\right)}\right)^{6} + 0.0714285714285714 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{8}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(351 \left(\operatorname{re}{\left(y\right)}\right)^{8} \operatorname{im}{\left(y\right)} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{6} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{4} \left(\operatorname{im}{\left(y\right)}\right)^{5} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{7} + 39 \left(\operatorname{im}{\left(y\right)}\right)^{9},39 \left(\operatorname{re}{\left(y\right)}\right)^{9} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{7} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{5} \left(\operatorname{im}{\left(y\right)}\right)^{4} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{3} \left(\operatorname{im}{\left(y\right)}\right)^{6} + 351 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{8} \right)}}{2} \right)} + 70.0999286732875 \left(\left(0.0714285714285714 \left(\operatorname{re}{\left(y\right)}\right)^{8} \operatorname{im}{\left(y\right)} - 0.666666666666667 \left(\operatorname{re}{\left(y\right)}\right)^{6} \left(\operatorname{im}{\left(y\right)}\right)^{3} + \left(\operatorname{re}{\left(y\right)}\right)^{4} \left(\operatorname{im}{\left(y\right)}\right)^{5} - 0.285714285714286 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{7} + 0.00793650793650794 \left(\operatorname{im}{\left(y\right)}\right)^{9}\right)^{2} + \left(0.00793650793650794 \left(\operatorname{re}{\left(y\right)}\right)^{9} - 0.285714285714286 \left(\operatorname{re}{\left(y\right)}\right)^{7} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{5} \left(\operatorname{im}{\left(y\right)}\right)^{4} - 0.666666666666667 \left(\operatorname{re}{\left(y\right)}\right)^{3} \left(\operatorname{im}{\left(y\right)}\right)^{6} + 0.0714285714285714 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{8}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(351 \left(\operatorname{re}{\left(y\right)}\right)^{8} \operatorname{im}{\left(y\right)} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{6} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{4} \left(\operatorname{im}{\left(y\right)}\right)^{5} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{7} + 39 \left(\operatorname{im}{\left(y\right)}\right)^{9},39 \left(\operatorname{re}{\left(y\right)}\right)^{9} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{7} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{5} \left(\operatorname{im}{\left(y\right)}\right)^{4} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{3} \left(\operatorname{im}{\left(y\right)}\right)^{6} + 351 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{8} \right)}}{2} \right)}\]\[\sqrt{39 \cdot {y}^{9}} = i \left(- \sqrt[4]{\left(351 \left(\operatorname{re}{\left(y\right)}\right)^{8} \operatorname{im}{\left(y\right)} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{6} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{4} \left(\operatorname{im}{\left(y\right)}\right)^{5} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{7} + 39 \left(\operatorname{im}{\left(y\right)}\right)^{9}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{9} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{7} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{5} \left(\operatorname{im}{\left(y\right)}\right)^{4} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{3} \left(\operatorname{im}{\left(y\right)}\right)^{6} + 351 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{8}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(351 \left(\operatorname{re}{\left(y\right)}\right)^{8} \operatorname{im}{\left(y\right)} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{6} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{4} \left(\operatorname{im}{\left(y\right)}\right)^{5} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{7} + 39 \left(\operatorname{im}{\left(y\right)}\right)^{9},39 \left(\operatorname{re}{\left(y\right)}\right)^{9} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{7} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{5} \left(\operatorname{im}{\left(y\right)}\right)^{4} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{3} \left(\operatorname{im}{\left(y\right)}\right)^{6} + 351 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{8} \right)}}{2} \right)}\right) - \sqrt[4]{\left(351 \left(\operatorname{re}{\left(y\right)}\right)^{8} \operatorname{im}{\left(y\right)} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{6} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{4} \left(\operatorname{im}{\left(y\right)}\right)^{5} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{7} + 39 \left(\operatorname{im}{\left(y\right)}\right)^{9}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{9} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{7} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{5} \left(\operatorname{im}{\left(y\right)}\right)^{4} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{3} \left(\operatorname{im}{\left(y\right)}\right)^{6} + 351 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{8}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(351 \left(\operatorname{re}{\left(y\right)}\right)^{8} \operatorname{im}{\left(y\right)} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{6} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{4} \left(\operatorname{im}{\left(y\right)}\right)^{5} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{7} + 39 \left(\operatorname{im}{\left(y\right)}\right)^{9},39 \left(\operatorname{re}{\left(y\right)}\right)^{9} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{7} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{5} \left(\operatorname{im}{\left(y\right)}\right)^{4} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{3} \left(\operatorname{im}{\left(y\right)}\right)^{6} + 351 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{8} \right)}}{2} \right)} \approx - 70.0999286732875 i \left(\left(0.0714285714285714 \left(\operatorname{re}{\left(y\right)}\right)^{8} \operatorname{im}{\left(y\right)} - 0.666666666666667 \left(\operatorname{re}{\left(y\right)}\right)^{6} \left(\operatorname{im}{\left(y\right)}\right)^{3} + \left(\operatorname{re}{\left(y\right)}\right)^{4} \left(\operatorname{im}{\left(y\right)}\right)^{5} - 0.285714285714286 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{7} + 0.00793650793650794 \left(\operatorname{im}{\left(y\right)}\right)^{9}\right)^{2} + \left(0.00793650793650794 \left(\operatorname{re}{\left(y\right)}\right)^{9} - 0.285714285714286 \left(\operatorname{re}{\left(y\right)}\right)^{7} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{5} \left(\operatorname{im}{\left(y\right)}\right)^{4} - 0.666666666666667 \left(\operatorname{re}{\left(y\right)}\right)^{3} \left(\operatorname{im}{\left(y\right)}\right)^{6} + 0.0714285714285714 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{8}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(351 \left(\operatorname{re}{\left(y\right)}\right)^{8} \operatorname{im}{\left(y\right)} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{6} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{4} \left(\operatorname{im}{\left(y\right)}\right)^{5} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{7} + 39 \left(\operatorname{im}{\left(y\right)}\right)^{9},39 \left(\operatorname{re}{\left(y\right)}\right)^{9} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{7} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{5} \left(\operatorname{im}{\left(y\right)}\right)^{4} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{3} \left(\operatorname{im}{\left(y\right)}\right)^{6} + 351 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{8} \right)}}{2} \right)} - 70.0999286732875 \left(\left(0.0714285714285714 \left(\operatorname{re}{\left(y\right)}\right)^{8} \operatorname{im}{\left(y\right)} - 0.666666666666667 \left(\operatorname{re}{\left(y\right)}\right)^{6} \left(\operatorname{im}{\left(y\right)}\right)^{3} + \left(\operatorname{re}{\left(y\right)}\right)^{4} \left(\operatorname{im}{\left(y\right)}\right)^{5} - 0.285714285714286 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{7} + 0.00793650793650794 \left(\operatorname{im}{\left(y\right)}\right)^{9}\right)^{2} + \left(0.00793650793650794 \left(\operatorname{re}{\left(y\right)}\right)^{9} - 0.285714285714286 \left(\operatorname{re}{\left(y\right)}\right)^{7} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{5} \left(\operatorname{im}{\left(y\right)}\right)^{4} - 0.666666666666667 \left(\operatorname{re}{\left(y\right)}\right)^{3} \left(\operatorname{im}{\left(y\right)}\right)^{6} + 0.0714285714285714 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{8}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(351 \left(\operatorname{re}{\left(y\right)}\right)^{8} \operatorname{im}{\left(y\right)} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{6} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{4} \left(\operatorname{im}{\left(y\right)}\right)^{5} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{7} + 39 \left(\operatorname{im}{\left(y\right)}\right)^{9},39 \left(\operatorname{re}{\left(y\right)}\right)^{9} - 1404 \left(\operatorname{re}{\left(y\right)}\right)^{7} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4914 \left(\operatorname{re}{\left(y\right)}\right)^{5} \left(\operatorname{im}{\left(y\right)}\right)^{4} - 3276 \left(\operatorname{re}{\left(y\right)}\right)^{3} \left(\operatorname{im}{\left(y\right)}\right)^{6} + 351 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{8} \right)}}{2} \right)}\]