I am a mechanical engineer who hasn't done any mechanical engineering for close to 20 years & hence forgotten all Mechanical Engineering & all Engineering Mathematics. I need to revise on some Engineering Math now - Calculus, Laplace Transforms etc. I have been doing it for a couple of days. I am getting stuck in a discussion of Complex Variables & Complex functions in Laplace Transforms. G(s) = 1/(s+1) We are trying to check if this satisfies Cachy-Reimann & hence analytic. This is how the analysis goes in the notes I am referring to G(σ + jω) = 1/(σ + jω + 1) = Gx + jGy ---------- (1) From this, the next line says "where Gx = (σ + 1)/ ( (σ + 1)2 + ω2) Gy = (-ω)/( (σ + 1)2 + ω2) " I don't see how you get Gx & Gy from (1) Can someone help? If this is based on some other Math stuff which I need to study before getting here, do let me know.