# How to plot a sequence of complex numbers?

I want to plot the complex sequence of numbers $$(1/(1 + I))^n$$ so that I can roughly see divergence/convergence. I tried DiscretePlot but doesn't seem to work.

• There are many ways to do this. One example is plotting-complex-numbers Nov 29 '19 at 9:43
• Write the complex sequence in polar form: $$1/\exp{( n * i * \pi / 4 )} / \sqrt{ 2 }^n \,\,.$$ The sequence spirals around and approaches zero. Nov 29 '19 at 10:12

You can use the new in M12 function ComplexListPlot:

ComplexListPlot[Table[(1/(1+I))^n, {n, 10}]]


In earlier versions you can use ListPlot:

ListPlot[Table[ReIm[1/(1+I)^n], {n, 10}]]


If you want a continuous curve, you can use ParametricPlot:

ParametricPlot[ReIm[1/(1+I)^n], {n, 0, 10}]


I would be tempted to plot this in magnitude and phase:

c = Table[(1/(1 + I))^n, {n, 25}];
ListPlot[{Abs[c], Arg[c]}]


You can see the convergence of the magnitude to zero and the phase constantly decreasing with constant slope.