Hi Sara, I'm not sure what A has to do with the way you have phrased your question. The span of b is simply all scalar multiples of b. Accordingly, it's just the imaginary axis.
Or did you really mean to ask whether b is in the range of A, in other words, in the span of the columns of A? In that case, did you really mean that b = [0; 1j]?
There is a difference between the following two vector spaces, the complex numbers, C, and complex-vectors with two entries, C^2.
The columns of A are vectors in C^2. The "vector" b as you have written it is just in C.
