1
$\begingroup$

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.

$\endgroup$
2
  • 1
    $\begingroup$ There are many ways to do this. One example is plotting-complex-numbers $\endgroup$
    – Nasser
    Commented Nov 29, 2019 at 9:43
  • 4
    $\begingroup$ Write the complex sequence in polar form: $$1/\exp{( n * i * \pi / 4 )} / \sqrt{ 2 }^n \,\,.$$ The sequence spirals around and approaches zero. $\endgroup$
    – LouisB
    Commented Nov 29, 2019 at 10:12

2 Answers 2

5
$\begingroup$

You can use the new in M12 function ComplexListPlot:

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

enter image description here

In earlier versions you can use ListPlot:

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

enter image description here

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

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

enter image description here

$\endgroup$
2
$\begingroup$

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

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

enter image description here

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.