Plot of the geometric-series' amplitude in the x+iy complex-plane, with linear-complex colorization where red is 1, chartreuse is i, cyan is -1, and indigo is -i. The only pole is located rightward of center at x+iy ⇒ 1, while x+iy ⇒ i is located above center. The Taylor series model only converges for |x+iy|<1 i.e. inside the second to smallest dashed circle, even though the distributive model function for the infinite power-series Σj(x+iy)j = 1/(1-(x+iy)) is analytic everywhere except at x+iy ⇒ 1.