HP 48G - Manual (Page 38)

Lesson 10: Arithmetic with Complex Numbers
The complex-number capabilities of the 111’ 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 scpiare root of -4.
4 m m 1 = (
0
,
2
)
SBEÓ313
The answer is a
c o m p l e x n u m b e r
—displayed as an ordered pair. The
first term is the real component and the second is the imaginary
component. This answer is 0 + 2 i or just 2/ (the principal square root
of-4).
Complex numbers can l)e expressed in two forms: rectangular
(,r -b j/i) and polar ( r { c o s 6 4-isind) ). The HP 48 can handle both
forms, althougli they are entered as ordered pairs, (r,
y )
and (?•, f?),
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 sj'mbolic expressions.
Exaiiipie: Enter the number 3 +
4 i
(rectangular coordinates)
the fSPCl key to separate the two coordinates.
Use
Ifni 3 fSPCi 4 (ENTER I 1 ■ ______
(3,4)
BÉQSi
Example: Enter the number with magnitude 5.39 and phase 158.2
degrees (polar coordinates).
S t e p 1 :
(tí
S3
Set the angle mode to Degrees, then type in the number.
(Note that the A- character is located above the (SPC) key.)
(D(3D OK
' [¿3 158.2
1: (3,4)
(5.39^158.2)
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3-10 Arithmetic