# Complex Numbers


```python
import sympy as sym
sym.init_printing()
import sympy.vector as sv

x, y, z, t = sym.symbols('x,y,z,t')
R= sv.CoordSys3D('R') # cf ReferenceFrame of sympy.physics.vector

def v(x,y,z): # vector field as a function of scalar variables x,y,z
    return x*y*R.i + 2*y*z*R.j + 3*x*z*R.k

def voft(l): # vector field along path l as a function of t
    x,y,z = (l.dot(R.i),l.dot(R.j),l.dot(R.k)) # x,y,z as functions of t
    return v(x,y,z)

def li(l,v): # dl/dt
    dl = sym.diff(l,t)
    return sym.integrate(voft(l).dot(dl),(t,0,1))

l1 = 2*t*R.j
l2 = 2*(1-t)*R.j + 2*t*R.k
l3 = 2*(1-t)*R.k
```


```python

```

ae70410d5e96165310c9ab63b5de27b108157ec2
ipynb
Jupyter Notebook
src/complex_numbers.ipynb
rsouza01/mathematical_physics_python
5c9a953e5930242f5f1adecf968d4b7be215c6d7
MIT
src/complex_numbers.ipynb
rsouza01/mathematical_physics_python
5c9a953e5930242f5f1adecf968d4b7be215c6d7
MIT
src/complex_numbers.ipynb
rsouza01/mathematical_physics_python
5c9a953e5930242f5f1adecf968d4b7be215c6d7
MIT
Qwen/Qwen-72B
1. YES
2. YES