sqrt((8x-24)/(((1)/(2)x)+5))

asked by guest
on Sep 20, 2024 at 8:38 am



You asked:

Evaluate the expression: \(\sqrt{\frac{8 x - 24}{\frac{1}{2 x} + 5}}\)

MathBot Answer:

Evaluated



\(\displaystyle \sqrt{\frac{8 x - 24}{\frac{1}{2 x} + 5}} = \sqrt{\frac{8 x - 24}{5 + \frac{1}{2 x}}} \)

Expanded

\[\sqrt{\frac{8 x - 24}{\frac{1}{2 x} + 5}} = \sqrt{\frac{8 x}{5 + \frac{1}{2 x}} - \frac{24}{5 + \frac{1}{2 x}}}\]

Factored

\[\sqrt{\frac{8 x - 24}{\frac{1}{2 x} + 5}} = 4 \sqrt{\frac{x \left(x - 3\right)}{10 x + 1}}\]

Roots

\[\sqrt{\frac{8 x - 24}{\frac{1}{2 x} + 5}} = i \left(- 4 \sqrt[4]{\left(\frac{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \left(10 \operatorname{re}{\left(x\right)} + 1\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{10 \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\frac{10 \cdot \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(10 \operatorname{re}{\left(x\right)} + 1\right) \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \left(10 \operatorname{re}{\left(x\right)} + 1\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{10 \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{10 \cdot \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(10 \operatorname{re}{\left(x\right)} + 1\right) \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}\right) - 4 \sqrt[4]{\left(\frac{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \left(10 \operatorname{re}{\left(x\right)} + 1\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{10 \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\frac{10 \cdot \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(10 \operatorname{re}{\left(x\right)} + 1\right) \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \left(10 \operatorname{re}{\left(x\right)} + 1\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{10 \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{10 \cdot \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(10 \operatorname{re}{\left(x\right)} + 1\right) \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} \approx - 12.6491106406735 i \left(\left(\frac{0.1 \cdot \left(2.0 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3.0 \operatorname{im}{\left(x\right)}\right) \left(10.0 \operatorname{re}{\left(x\right)} + 1.0\right)}{100.0 \left(- \operatorname{re}{\left(x\right)} - 0.1\right)^{2} + 100.0 \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3.0 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)}}{100.0 \left(- \operatorname{re}{\left(x\right)} - 0.1\right)^{2} + 100.0 \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\frac{\left(2.0 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3.0 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{100.0 \left(- \operatorname{re}{\left(x\right)} - 0.1\right)^{2} + 100.0 \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{0.1 \cdot \left(10.0 \operatorname{re}{\left(x\right)} + 1.0\right) \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3.0 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}{100.0 \left(- \operatorname{re}{\left(x\right)} - 0.1\right)^{2} + 100.0 \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \left(10 \operatorname{re}{\left(x\right)} + 1\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{10 \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{10 \cdot \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(10 \operatorname{re}{\left(x\right)} + 1\right) \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} - 12.6491106406735 \left(\left(\frac{0.1 \cdot \left(2.0 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3.0 \operatorname{im}{\left(x\right)}\right) \left(10.0 \operatorname{re}{\left(x\right)} + 1.0\right)}{100.0 \left(- \operatorname{re}{\left(x\right)} - 0.1\right)^{2} + 100.0 \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3.0 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)}}{100.0 \left(- \operatorname{re}{\left(x\right)} - 0.1\right)^{2} + 100.0 \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\frac{\left(2.0 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3.0 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{100.0 \left(- \operatorname{re}{\left(x\right)} - 0.1\right)^{2} + 100.0 \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{0.1 \cdot \left(10.0 \operatorname{re}{\left(x\right)} + 1.0\right) \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3.0 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}{100.0 \left(- \operatorname{re}{\left(x\right)} - 0.1\right)^{2} + 100.0 \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \left(10 \operatorname{re}{\left(x\right)} + 1\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{10 \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{10 \cdot \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(10 \operatorname{re}{\left(x\right)} + 1\right) \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}\]\[\sqrt{\frac{8 x - 24}{\frac{1}{2 x} + 5}} = i 4 \sqrt[4]{\left(\frac{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \left(10 \operatorname{re}{\left(x\right)} + 1\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{10 \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\frac{10 \cdot \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(10 \operatorname{re}{\left(x\right)} + 1\right) \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \left(10 \operatorname{re}{\left(x\right)} + 1\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{10 \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{10 \cdot \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(10 \operatorname{re}{\left(x\right)} + 1\right) \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} + 4 \sqrt[4]{\left(\frac{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \left(10 \operatorname{re}{\left(x\right)} + 1\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{10 \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\frac{10 \cdot \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(10 \operatorname{re}{\left(x\right)} + 1\right) \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \left(10 \operatorname{re}{\left(x\right)} + 1\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{10 \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{10 \cdot \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(10 \operatorname{re}{\left(x\right)} + 1\right) \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} \approx 12.6491106406735 i \left(\left(\frac{0.1 \cdot \left(2.0 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3.0 \operatorname{im}{\left(x\right)}\right) \left(10.0 \operatorname{re}{\left(x\right)} + 1.0\right)}{100.0 \left(- \operatorname{re}{\left(x\right)} - 0.1\right)^{2} + 100.0 \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3.0 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)}}{100.0 \left(- \operatorname{re}{\left(x\right)} - 0.1\right)^{2} + 100.0 \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\frac{\left(2.0 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3.0 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{100.0 \left(- \operatorname{re}{\left(x\right)} - 0.1\right)^{2} + 100.0 \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{0.1 \cdot \left(10.0 \operatorname{re}{\left(x\right)} + 1.0\right) \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3.0 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}{100.0 \left(- \operatorname{re}{\left(x\right)} - 0.1\right)^{2} + 100.0 \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \left(10 \operatorname{re}{\left(x\right)} + 1\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{10 \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{10 \cdot \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(10 \operatorname{re}{\left(x\right)} + 1\right) \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} + 12.6491106406735 \left(\left(\frac{0.1 \cdot \left(2.0 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3.0 \operatorname{im}{\left(x\right)}\right) \left(10.0 \operatorname{re}{\left(x\right)} + 1.0\right)}{100.0 \left(- \operatorname{re}{\left(x\right)} - 0.1\right)^{2} + 100.0 \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3.0 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)}}{100.0 \left(- \operatorname{re}{\left(x\right)} - 0.1\right)^{2} + 100.0 \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\frac{\left(2.0 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3.0 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{100.0 \left(- \operatorname{re}{\left(x\right)} - 0.1\right)^{2} + 100.0 \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{0.1 \cdot \left(10.0 \operatorname{re}{\left(x\right)} + 1.0\right) \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3.0 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}{100.0 \left(- \operatorname{re}{\left(x\right)} - 0.1\right)^{2} + 100.0 \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \left(10 \operatorname{re}{\left(x\right)} + 1\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{10 \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{10 \cdot \left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - 3 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(10 \operatorname{re}{\left(x\right)} + 1\right) \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \operatorname{re}{\left(x\right)} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}{\left(- 10 \operatorname{re}{\left(x\right)} - 1\right)^{2} + 100 \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}\]

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