What is the phasor form for an E field with a variable distance and phase shift?

[cutesteph]

If I am given an E field E = uniti Asin[w(t-z/c)+pi/4].
Is the phasor form = unit i Aexp(j pi/4) or unit i Aexp(-j(wz/c - pi/4) ?

 

[rude man]

The phasor of a function (wave) containing variables other than time, in this case distance z, is I believe represented by a function including z but not t.

So the phasor of A cos(wt - kz) would be A exp(-jkz) as the time function is Re{A exp j(wt - kz)}. The exp(jwt) is left out of the phasor expression since in any equation using phasors that term cancels out. At least that's been my experience with e-m wave phasors.

So if the time function is A sin(wt - kz + θ), what do you think the phasor is?
Hint: change your time function to read A cos(wt - kz + ψ).