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Polar Representation Of A Complex Number - HP 50g User Manual

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Polar representation of a complex number

The polar representation of the complex number 3.5-1.2i, entered above,
is obtained by changing the coordinate system to cylindrical or polar
(using function CYLIN).
You can find this function in the catalog
(‚N). You can also change the coordinate to polar using H.
Changing to polar coordinate with standard notation and the angular
measure in radians, produces the result in RPN mode:
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
i
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,
). The angle
symbol ( ) can be entered as ~‚6. For example, the complex
1.5i
number z = 5.2e
, can be entered as follows (the figures show the RPN
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
, y = r sin
, 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:
Page 4-3

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