Polar representation of a complex number
The result shown above represents a Cartesian (rectangular) representation of
the complex number 3.5-1.2i. A polar representation is possible if we
change the coordinate system to cylindrical or polar, by using function CYLIN.
You can find this function in the catalog (‚N). Changing to polar
shows the result:
For this result the angular measure is set to radians (you can always change to
radians by using function RAD). The result shown above represents a
magnitude, 3.7, and an angle 0.33029.... The angle symbol (∠) is shown in
front of the angle measure.
Return to Cartesian or rectangular coordinates by using function RECT
(available in the catalog, ‚N). A complex number in polar
representation is written as z = r⋅e
. You can enter this complex number into
the calculator by using an ordered pair of the form (r, ∠θ). The angle symbol
(∠) can be entered as ~‚6.
For example, the complex number z =
, can be entered as follows (the figures show the stack, before and
after entering the number):
Because the coordinate system is set to rectangular (or Cartesian), the
calculator automatically converts the number entered to Cartesian coordinates,
i.e., x = r cos θ, y = r sin θ, resulting, for this case, in (0.3678..., 5.18...).
On the other hand, if the coordinate system is set to cylindrical coordinates
(use CYLIN), entering a complex number (x,y), where x and y are real
numbers, will produce a polar representation. For example, in cylindrical
coordinates, enter the number (3.,2.). The figure below shows the RPN stack,
before and after entering this number: