Lesson 10: arithmetic with complex numbers, Lesson 10: arithmetic with cgmplex numbers – HP 48G User Manual
Page 38
Attention! The text in this document has been recognized automatically. To view the original document, you can use the "Original mode".
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)
Ka8IY»ll!88r;lil«iMigIiniM—HjTO
3-10 Arithmetic