In equations (5), (7), (8), (10), and (11), we advance the phase by the angle ϕ if we replace ωt by ωt+ϕ (that is, if we replace −ωt by −ωt−ϕ), with the result that the (complex) field is multiplied by e. So a phase advance is equivalent to multiplication by a complex constant with a negative argument. This becomes more obvious when (e.g.) the field (5) is factored as E k e i k ⋅ ⋅ r e − − i ω ω t , where the last factor contains the time-dependence.