Here, we present complex resonance states (or Siegert states) that describe the tunnelling decay of a trapped quantum particle from an intuitive point of view that naturally leads to the easily applicable Siegert approximation method. This can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear Schrodinger equations. This approach thus complements other treatments of the subject that mostly focus on methods based on continuation in the complex plane or on semiclassical approximations. (Contains 1 table and 1 figure.)