Needs["VectorAnalysis`"]
SetCoordinates[Spherical]
SetAttributes[k, Constant]
SetAttributes[omega, Constant]
SetAttributes[t, Constant]
bEphasor:={0,0,((1-I/(k * Rr)) E^(I k * Rr) Sin[Ttheta])/Rr}
bBphasor := -(I/k) Curl[bEphasor] E^(-I omega t)
bE :=Simplify[ComplexExpand[Simplify[Re[bEphasor], Element[{k,omega, t}, Reals]]]]
bB :=Simplify[ComplexExpand[Simplify[Re[bBphasor], Element[{k,omega, t}, Reals]]]]
bB

bE

Div[bE]

Simplify[Div[bB]]

k := omega
FullSimplify[Curl[bB] - D[bE, t]]

FullSimplify[Curl[bE] + D[bB, t]]

FullSimplify[Curl[bEphasor]- I omega bBphasor,Element[{k,omega, t}, Reals]]