Hi I've working on a computer program where I need to calculate some electric fields. I am referring to a thesis which provides these formulas. For eg: The electric field for a ray(plane wave actually) at a distance s from the reference point: E(s) = E(0) * exp(-jks) where E(s) = electric field at a distance s from the reference point. E(0) = electric field at reference point. s = distance travelled. k = wave number = 2 * PI / wavelength exp(-jks) as per my thesis, represents the phase variation of the electric field along the ray. now, electric field is always a vector(3d in my case). so the user will input a magnitude for the electric field at the reference point and i can calculate the reference electric field vector[ E(0) ] easily by multiplying it with the unit direction vector the wave. exp(-jks) expands as cos(ks) - j sin(ks) ^ ^ ^ if E(0) is a vector of the form a x + b y + c z, ^ ^ ^ Then E(s) = (a x + b y + c z) * ( cos(ks) - j sin(ks) ) I'm really confounded at this expression because how does one multiply a complex number and a vector ? And even if it is possible then what about E(s) ? If E(0) was defined to be a 3d vector then E(s) must also be a 3d vector. What does it actually mean ? If there are some EE/ physics experts who can probably figure it out then it would be really great.