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.