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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
i
θ
. 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 =
5.2e
1.5i
, 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: