Can you determine the sign of the polar form of a complex number?

[Jason]

On Oct 17, 7:51 am, schaefer... at gmail.com wrote:
> Just to clarify what I'm after:
>
> If you plot (-3)^n where n is a set of negative real numbers between 0
> and -20 for example, then you get a discontinuos line due to the
> problem mentioned above with fractional exponents. However, you can
> compute what the correct absolute value of the the missing points
> should be (see z2 above for an example), but I would like to know how
> to determine what the correct sign of z2 should be so that it fits the
> graph.

As Roy said, a math newsgroup may be able to help you better, as you
seem to be having fundamental issues with imaginary numbers.  The
imaginary part isn't an artifact of computing (-3+0j)**(-4.5), it is
an integral part of the answer.  Without the imaginary part, the
result is very, very incorrect.

Actually, the graph result of (-3)^n is not necessarily discontinuous
at the intervals you specified.  You just need to graph the result
with the proper number of dimensions.  If you want to plot the results
of (-3)^n for n=0 to -20, you need to make a three dimensional graph,
a two dimensional graph with two sets of lines, or a circular graph
with labeled values of n.

Complex numbers can be viewed as having a magnitude and a rotation in
the real/imaginary plane.  This is called polar form.  Complex numbers
can also be represented using a Cartesian form, which is how Python
displays complex numbers.

Python's complex numbers allow you to extract the real or imaginary
part separately, via the "real" and "imag" attributes.  To convert to
polar form, you'll need to use the abs built-in to retrieve the
magnitude, and math.atan2 to retrieve the angle.  (Remember that the
imaginary part is considered the Y-axis component.)

Depending on what you're doing, you might need the real part or the
magnitude.  It sounds a little bit like you're trying to represent
something as a flatlander when you should be in Spaceland.  (http://
en.wikipedia.org/wiki/Flatland)

  --Jason