Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

In an ebook about elementary complex analysis I came across Newton's law of universal gravitation with a complex valued function in place of $r(t)$. Can somebody please explain the intuition about how a real valued function gets translated into a complex function $z(t)$? I don't understand how this was done. Thanks! (I think this might be a pretty illustrative way to connect real and complex functions, so I thought I'd put it up.)

enter image description here

share|cite|improve this question

The ebook considers the orbit plane


of the body as a complex plane, and introduces complex coordinates


and complex force


If one rewrites in real and imaginary parts, one recovers the the usual component-wise real formulation of Newton's gravitation law.

share|cite|improve this answer
Correction to v2: 'the the' in last line should be 'the'. – Qmechanic Feb 20 '13 at 1:09

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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