Solutions of maxwells equations in Vaccum

Homework Statement

Show that the Fields E= Eo exp{i (k.r-ωt)} and B= Bo exp{i(k.r-ωt) are solutions of Maxwell's Equations in source free vaccum.Starting with maxwells equations in vaccum.
And there by Derive the relations between the Magnitudes & Phases of
Eo, Bo, ω, k, & c. And the directions of Unit vectors Eo,Bo,& k.

Hint( Should only need the fact that Del (k.r) = k .

Homework Equations

Div E = 0.

Div B = 0.

Curl E= - (1/c)d/dt(B)

curl B = (1/c) d/dt(E).

atempt at a solution[/b]

How to solve these Equations. to obtain the Electric & Magnetic Feilds.

Atleast give me Hint.. how to start this..

iam really trying hard on this...

Here's your first hint: read the question. (I've found that to be pretty useful myself) "Show that the fields $$\vec{E} = \vec{E}_0 e^{i(\vec{k}\cdot\vec{r} - \omega t)}$$ and $$\vec{B} = \vec{B}_0 e^{i(\vec{k}\cdot\vec{r} - \omega t)}$$ are solutions of Maxwell's equations..." Surely you can do that? Just plug them in and see what you get.