Hertzian diople, magnetic field and relation to Maxwell's equations

[kings]

Homework Statement

Show how the given physical magnetic field is consistent with a monochromatic plane wave solution to Maxwell equation

Homework Equations

[/B]
Physical:
> B_phys(t) = B₀ sin (2πft) e_x

Maxwells:
> B = iB₀ exp[i(kz − ωt)] e_x.

The Attempt at a Solution

I know that field is the real part of maxwells equation but I am struggling to find how to can work out how to get from one to the other?
I also got that ω=2πf and k = ω/c
Am i heading the right direction?

 

[kuruman]

What is i ($=\sqrt{-1}$) written in terms of an exponential?