Complex numbers in sympy - sympy

Question

I am using lcapy together with sympy and trying to process complex numbers from a circuit.
I have the following sympy expression:
import sympy
from lcapy import j
expr = sympy.parse_expr('L*w_0*(C*R*w_0 - I)')
expr
Output:
L⋅w₀⋅(C⋅R⋅w₀ - ⅉ)
expr above is an complex expression with ⅉ being the imaginary number. Can I use sympy and remove the brackets from expr in order to view it in the more canonical form for complex numbers as
w₀^2⋅R⋅L⋅C - ⅉ⋅w₀⋅L
And does sympy have support for handling complex numbers? I want to get the argument of expr which should be:
arctan(L⋅w₀ / w₀^2⋅R⋅L⋅C)

Answer 1

I can do (in an isympy session):
In [13]: expr
Out[13]: L⋅w₀⋅(C⋅R⋅w₀ - ⅈ)
In [14]: expr.expand()
Out[14]:
2
C⋅L⋅R⋅w₀ - ⅈ⋅L⋅w₀
edit
try
atan2(im(expr), re(expr))
https://docs.sympy.org/latest/modules/functions/elementary.html
Refining the variables:
In [53]: C,L,R,w_0=symbols('C L R w_0',real=True, positive=True)
In [54]: expr=L*w_0*(C*R*w_0-I)
In [55]: expr
Out[55]: L⋅w₀⋅(C⋅R⋅w₀ - ⅈ)
In [56]: expr.expand()
Out[56]:
2
C⋅L⋅R⋅w₀ - ⅈ⋅L⋅w₀
In [57]: im(_),re(_)
Out[57]:
⎛ 2⎞
⎝-L⋅w₀, C⋅L⋅R⋅w₀ ⎠
Now the atan2 is simplified:
In [59]: atan2(*_)
Out[59]:
⎛ 1 ⎞
-atan⎜──────⎟
⎝C⋅R⋅w₀⎠
And arg does the same:
In [60]: arg(_56)
Out[60]: arg(C⋅R⋅w₀ - ⅈ)
In [62]: arg(expr)
Out[62]: arg(C⋅R⋅w₀ - ⅈ)
In [77]: arg(expr)._eval_rewrite_as_atan2(expr)
Out[77]:
⎛ 1 ⎞
-atan⎜──────⎟
⎝C⋅R⋅w₀⎠