```python
import numpy as np
import sympy as sy
import matplotlib.pyplot as plt
%matplotlib inline
```


```python
s = sy.symbols('s', real=False)
A2 = s**2 + 3*s + 3
A4 = s**4 + 10*s**3 + 45*s**2 + 105*s + 105
A22= sy.simplify(sy.expand(A2*A2))
```


```python
sol22 = sy.solve(A22, s)
sol4 = sy.solve(A4, s)

```


```python
sol22
```




    [-3/2 - sqrt(3)*I/2, -3/2 + sqrt(3)*I/2]




```python
sol4
```




    [-5/2 - sqrt(-5 + 15/(2*(-75/16 + 15*sqrt(35)*I/16)**(1/3)) + 2*(-75/16 + 15*sqrt(35)*I/16)**(1/3))/2 - sqrt(-10 - 2*(-75/16 + 15*sqrt(35)*I/16)**(1/3) + 10/sqrt(-5 + 15/(2*(-75/16 + 15*sqrt(35)*I/16)**(1/3)) + 2*(-75/16 + 15*sqrt(35)*I/16)**(1/3)) - 15/(2*(-75/16 + 15*sqrt(35)*I/16)**(1/3)))/2,
     -5/2 + sqrt(-10 - 2*(-75/16 + 15*sqrt(35)*I/16)**(1/3) + 10/sqrt(-5 + 15/(2*(-75/16 + 15*sqrt(35)*I/16)**(1/3)) + 2*(-75/16 + 15*sqrt(35)*I/16)**(1/3)) - 15/(2*(-75/16 + 15*sqrt(35)*I/16)**(1/3)))/2 - sqrt(-5 + 15/(2*(-75/16 + 15*sqrt(35)*I/16)**(1/3)) + 2*(-75/16 + 15*sqrt(35)*I/16)**(1/3))/2]




```python
for r in sol22:
    plt.plot(sy.N(sy.re(r)), sy.N(sy.im(r)), 'x', markersize=12)
    
for r in sol4:
    plt.plot(np.real(sy.N(r)), np.imag(sy.N(r)), 'x', markersize=12)
    
    
```


```python

```

ac42e2caac2165c9ffe52eaee16cde9b9d4d9175
ipynb
Jupyter Notebook
sampling-and-aliasing/notebooks/PS7-Bessel-filters.ipynb
kjartan-at-tec/mr2007-computerized-control
16e35f5007f53870eaf344eea1165507505ab4aa
MIT
2020-11-07T05:20:37.000Z
2020-12-22T09:46:13.000Z
sampling-and-aliasing/notebooks/PS7-Bessel-filters.ipynb
alfkjartan/control-computarizado
5b9a3ae67602d131adf0b306f3ffce7a4914bf8e
MIT
2020-06-12T20:44:41.000Z
2020-06-12T20:49:00.000Z
sampling-and-aliasing/notebooks/PS7-Bessel-filters.ipynb
kjartan-at-tec/mr2007-computerized-control
16e35f5007f53870eaf344eea1165507505ab4aa
MIT
2021-03-14T03:55:27.000Z
2021-03-14T03:55:27.000Z
Qwen/Qwen-72B
1. YES
2. YES