A c-number coefficient like exp(1.0im*ωl*t) on an operator is expanded to cos(ωl·t)*exp(0) + exp(0)*im*sin(ωl·t) at construction time, so equations show sin/cos (plus a stray exp(0)) instead of e^{iω_l t}.

MWE:

using Symbolics
@variables ωl t
exp(1.0im*ωl*t)
# cos(t*ωl)*exp(0) + exp(0)*im*sin(t*ωl)

1.0im*ωl*t is a Complex{Num} (real 0, imag t*ωl), so exp dispatches to Julia Base's exp(::Complex) = exp(re)*(cos(im)+i*sin(im)). Current Symbolics (v7.x) represents every complex symbolic as Complex{Num}, so any exp of a complex argument is split. Older Symbolics kept it as a single node and printed e^{…}. Happens before any SQA/QC code runs.

Cosmetic only, e^{iθ} ≡ cos θ + i sin θ, numerics are identical. But it makes operator equations and docs (e.g. the heterodyne-detection example) hard to read.