Matrix in SymbolicUtils?

Probably answers most of it:

using ModelingToolkit

@variables x a b r θ

x + im * a

x = r*cos(θ) + im*r*sin(θ)

x.op # +
x.args

2-element Array{Expression,1}:
          r * cos(θ)
 ((im) * r) * sin(θ)

@shashi would have to answer the polynomial part.