Hi All and sorry if this is too easy a question but here goes.... Sines, Cosines and the rest of the trig functions are the ratio of two lengths and thus are dimensionless quantities. That is if I plug in a value for t in sin(ωt) there are no units. For example the solution of x'' + ω^2 x = 0 with x(0) = x0 and x'(0) = v0 is given by x(t) = x0 cos(ωt) + v0/ω sin(ωt) The units come from the initial conditions not the sine or cosine. So here is the question... Same is true ( I believe ) when using the natural exponential function exp(t). How does one simply explain this. I tried to reason it out using eulers formula exp(iω) = cos(ω) + i sin(ω) figuring that again we get ratios of lengths, however in the case where the real part is non-zero we get another exponential (which is not the ratio of lengths) exp(a +ib) = exp(a)(cos(b) + i sin(b)) Is there a simple explaination as to why we "lose the units" when using the exponential function?