$\sqrt{650x^{4}+2180x^{3}y+2940x^{2}y^{2}+1760xy^{3}+400y^{4} }$
You asked:
MathBot Answer:
Evaluated
\(\displaystyle \sqrt{650 \cdot {x}^{4} + 2180 \cdot {x}^{3} \cdot y + 2940 \cdot {x}^{2} \cdot {y}^{2} + 1760 x \cdot {y}^{3} + 400 \cdot {y}^{4}} = \sqrt{650 x^{4} + 2180 x^{3} y + 2940 x^{2} y^{2} + 1760 y^{3} x + 400 y^{4}} \)
Expanded
\[\sqrt{650 \cdot {x}^{4} + 2180 \cdot {x}^{3} \cdot y + 2940 \cdot {x}^{2} \cdot {y}^{2} + 1760 x \cdot {y}^{3} + 400 \cdot {y}^{4}} = \sqrt{650 x^{4} + 2180 x^{3} y + 2940 x^{2} y^{2} + 1760 y^{3} x + 400 y^{4}}\]
Factored
\[\sqrt{650 \cdot {x}^{4} + 2180 \cdot {x}^{3} \cdot y + 2940 \cdot {x}^{2} \cdot {y}^{2} + 1760 x \cdot {y}^{3} + 400 \cdot {y}^{4}} = \sqrt{10} \sqrt{\left(5 x^{2} + 6 x y + 2 y^{2}\right) \left(13 x^{2} + 28 x y + 20 y^{2}\right)}\]
Roots
\[\sqrt{650 \cdot {x}^{4} + 2180 \cdot {x}^{3} \cdot y + 2940 \cdot {x}^{2} \cdot {y}^{2} + 1760 x \cdot {y}^{3} + 400 \cdot {y}^{4}} = i \sqrt[4]{\left(2600 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 2600 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + 1600 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 1600 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 2940 \operatorname{im}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{im}{\left(x^{3} y\right)} + 1760 \operatorname{im}{\left(y^{3} x\right)}\right)^{2} + \left(650 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 3900 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 2940 \operatorname{re}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{re}{\left(x^{3} y\right)} + 1760 \operatorname{re}{\left(y^{3} x\right)} + 650 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 400 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2600 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 2600 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + 1600 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 1600 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 2940 \operatorname{im}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{im}{\left(x^{3} y\right)} + 1760 \operatorname{im}{\left(y^{3} x\right)},650 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 3900 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 2940 \operatorname{re}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{re}{\left(x^{3} y\right)} + 1760 \operatorname{re}{\left(y^{3} x\right)} + 650 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 400 \left(\operatorname{im}{\left(y\right)}\right)^{4} \right)}}{2} \right)} + \sqrt[4]{\left(2600 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 2600 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + 1600 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 1600 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 2940 \operatorname{im}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{im}{\left(x^{3} y\right)} + 1760 \operatorname{im}{\left(y^{3} x\right)}\right)^{2} + \left(650 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 3900 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 2940 \operatorname{re}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{re}{\left(x^{3} y\right)} + 1760 \operatorname{re}{\left(y^{3} x\right)} + 650 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 400 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2600 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 2600 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + 1600 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 1600 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 2940 \operatorname{im}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{im}{\left(x^{3} y\right)} + 1760 \operatorname{im}{\left(y^{3} x\right)},650 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 3900 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 2940 \operatorname{re}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{re}{\left(x^{3} y\right)} + 1760 \operatorname{re}{\left(y^{3} x\right)} + 650 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 400 \left(\operatorname{im}{\left(y\right)}\right)^{4} \right)}}{2} \right)} \approx 62.449979983984 i \left(0.568284023668639 \left(0.884353741496599 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 0.884353741496599 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + 0.54421768707483 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 0.54421768707483 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + \operatorname{im}{\left(x^{2} y^{2}\right)} + 0.741496598639456 \operatorname{im}{\left(x^{3} y\right)} + 0.598639455782313 \operatorname{im}{\left(y^{3} x\right)}\right)^{2} + \left(0.166666666666667 \left(\operatorname{re}{\left(x\right)}\right)^{4} - \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 0.102564102564103 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 0.615384615384615 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 0.753846153846154 \operatorname{re}{\left(x^{2} y^{2}\right)} + 0.558974358974359 \operatorname{re}{\left(x^{3} y\right)} + 0.451282051282051 \operatorname{re}{\left(y^{3} x\right)} + 0.166666666666667 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 0.102564102564103 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2600 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 2600 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + 1600 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 1600 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 2940 \operatorname{im}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{im}{\left(x^{3} y\right)} + 1760 \operatorname{im}{\left(y^{3} x\right)},650 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 3900 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 2940 \operatorname{re}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{re}{\left(x^{3} y\right)} + 1760 \operatorname{re}{\left(y^{3} x\right)} + 650 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 400 \left(\operatorname{im}{\left(y\right)}\right)^{4} \right)}}{2} \right)} + 62.449979983984 \left(0.568284023668639 \left(0.884353741496599 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 0.884353741496599 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + 0.54421768707483 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 0.54421768707483 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + \operatorname{im}{\left(x^{2} y^{2}\right)} + 0.741496598639456 \operatorname{im}{\left(x^{3} y\right)} + 0.598639455782313 \operatorname{im}{\left(y^{3} x\right)}\right)^{2} + \left(0.166666666666667 \left(\operatorname{re}{\left(x\right)}\right)^{4} - \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 0.102564102564103 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 0.615384615384615 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 0.753846153846154 \operatorname{re}{\left(x^{2} y^{2}\right)} + 0.558974358974359 \operatorname{re}{\left(x^{3} y\right)} + 0.451282051282051 \operatorname{re}{\left(y^{3} x\right)} + 0.166666666666667 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 0.102564102564103 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2600 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 2600 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + 1600 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 1600 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 2940 \operatorname{im}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{im}{\left(x^{3} y\right)} + 1760 \operatorname{im}{\left(y^{3} x\right)},650 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 3900 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 2940 \operatorname{re}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{re}{\left(x^{3} y\right)} + 1760 \operatorname{re}{\left(y^{3} x\right)} + 650 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 400 \left(\operatorname{im}{\left(y\right)}\right)^{4} \right)}}{2} \right)}\]\[\sqrt{650 \cdot {x}^{4} + 2180 \cdot {x}^{3} \cdot y + 2940 \cdot {x}^{2} \cdot {y}^{2} + 1760 x \cdot {y}^{3} + 400 \cdot {y}^{4}} = i \left(- \sqrt[4]{\left(2600 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 2600 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + 1600 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 1600 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 2940 \operatorname{im}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{im}{\left(x^{3} y\right)} + 1760 \operatorname{im}{\left(y^{3} x\right)}\right)^{2} + \left(650 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 3900 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 2940 \operatorname{re}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{re}{\left(x^{3} y\right)} + 1760 \operatorname{re}{\left(y^{3} x\right)} + 650 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 400 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2600 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 2600 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + 1600 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 1600 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 2940 \operatorname{im}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{im}{\left(x^{3} y\right)} + 1760 \operatorname{im}{\left(y^{3} x\right)},650 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 3900 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 2940 \operatorname{re}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{re}{\left(x^{3} y\right)} + 1760 \operatorname{re}{\left(y^{3} x\right)} + 650 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 400 \left(\operatorname{im}{\left(y\right)}\right)^{4} \right)}}{2} \right)}\right) - \sqrt[4]{\left(2600 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 2600 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + 1600 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 1600 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 2940 \operatorname{im}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{im}{\left(x^{3} y\right)} + 1760 \operatorname{im}{\left(y^{3} x\right)}\right)^{2} + \left(650 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 3900 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 2940 \operatorname{re}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{re}{\left(x^{3} y\right)} + 1760 \operatorname{re}{\left(y^{3} x\right)} + 650 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 400 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2600 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 2600 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + 1600 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 1600 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 2940 \operatorname{im}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{im}{\left(x^{3} y\right)} + 1760 \operatorname{im}{\left(y^{3} x\right)},650 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 3900 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 2940 \operatorname{re}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{re}{\left(x^{3} y\right)} + 1760 \operatorname{re}{\left(y^{3} x\right)} + 650 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 400 \left(\operatorname{im}{\left(y\right)}\right)^{4} \right)}}{2} \right)} \approx - 62.449979983984 i \left(0.568284023668639 \left(0.884353741496599 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 0.884353741496599 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + 0.54421768707483 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 0.54421768707483 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + \operatorname{im}{\left(x^{2} y^{2}\right)} + 0.741496598639456 \operatorname{im}{\left(x^{3} y\right)} + 0.598639455782313 \operatorname{im}{\left(y^{3} x\right)}\right)^{2} + \left(0.166666666666667 \left(\operatorname{re}{\left(x\right)}\right)^{4} - \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 0.102564102564103 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 0.615384615384615 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 0.753846153846154 \operatorname{re}{\left(x^{2} y^{2}\right)} + 0.558974358974359 \operatorname{re}{\left(x^{3} y\right)} + 0.451282051282051 \operatorname{re}{\left(y^{3} x\right)} + 0.166666666666667 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 0.102564102564103 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2600 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 2600 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + 1600 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 1600 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 2940 \operatorname{im}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{im}{\left(x^{3} y\right)} + 1760 \operatorname{im}{\left(y^{3} x\right)},650 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 3900 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 2940 \operatorname{re}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{re}{\left(x^{3} y\right)} + 1760 \operatorname{re}{\left(y^{3} x\right)} + 650 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 400 \left(\operatorname{im}{\left(y\right)}\right)^{4} \right)}}{2} \right)} - 62.449979983984 \left(0.568284023668639 \left(0.884353741496599 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 0.884353741496599 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + 0.54421768707483 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 0.54421768707483 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + \operatorname{im}{\left(x^{2} y^{2}\right)} + 0.741496598639456 \operatorname{im}{\left(x^{3} y\right)} + 0.598639455782313 \operatorname{im}{\left(y^{3} x\right)}\right)^{2} + \left(0.166666666666667 \left(\operatorname{re}{\left(x\right)}\right)^{4} - \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 0.102564102564103 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 0.615384615384615 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 0.753846153846154 \operatorname{re}{\left(x^{2} y^{2}\right)} + 0.558974358974359 \operatorname{re}{\left(x^{3} y\right)} + 0.451282051282051 \operatorname{re}{\left(y^{3} x\right)} + 0.166666666666667 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 0.102564102564103 \left(\operatorname{im}{\left(y\right)}\right)^{4}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2600 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 2600 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + 1600 \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 1600 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + 2940 \operatorname{im}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{im}{\left(x^{3} y\right)} + 1760 \operatorname{im}{\left(y^{3} x\right)},650 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 3900 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 400 \left(\operatorname{re}{\left(y\right)}\right)^{4} - 2400 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 2940 \operatorname{re}{\left(x^{2} y^{2}\right)} + 2180 \operatorname{re}{\left(x^{3} y\right)} + 1760 \operatorname{re}{\left(y^{3} x\right)} + 650 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 400 \left(\operatorname{im}{\left(y\right)}\right)^{4} \right)}}{2} \right)}\]