HP 48gx User Manual

Lesson 10: Arithmetic with Complex Numbers
The complex-number capabilities of the HP 48 can affect the results of
real-number operations. Certain calculations that would result in an
error on most calculators yield valid complex results on the HP 48.
Example: Find the square root of -4.
ADB)
1:
(8,2)
[+-HAT[HAT] #0 [30m] | [APPLY]
The answer is a complex number—displayed as an ordered pair. The
first term is the real component and the second is the imaginary
component. This answer is 0 + 2¢ or just 2¢ (the principal square root
of -4).
Complex numbers can be expressed in two forms: rectangular
(z + yi) and polar ( r(cosf + isin) ). The HP 48 can handle both
forms, although they are entered as ordered pairs, (z,y) and (7,6),
respectively.
A complex number, like a real number, is a single object. Many
functions that work with real numbers also work with complex
numbers. You can use complex numbers as arguments for arithmetic
operations, and you can use them in symbolic expressions.
Example: Enter the number 3 + 4: (rectangular coordinates). Use
the key to separate the two coordinates.
3 (SPC) 4 (ENTER) 1: (3, 4)
&) EG EEL EEE EE ET CT
Example: Enter the number with magnitude 5.39 and phase 158.2
degrees (polar coordinates).
Step 1: Set the angle mode to Degrees, then type in the number.
(Note that the X character is located above the key.)
@®
(ones)
M@D
ok
:
——_
(3,4)
-
&
-
&
(539
@(=)
158.2
[+HMAT+
HAT]
#0
[#2]
|
[APPLY]
3-10 Arithmetic

HP 48gx Specifications

General

Brand	HP
Model	48gx
Category	Calculator
Language	English