Casio Fx991ms User Guide

E-9
Imaginary axis
Real axis
kAbsolute Value and Argument
Calculation
Supposing the imaginary number expressed by the
rectangular form z = a + bi is represented as a point in the
Gaussian plane, you can determine the absolute value (r)
and argument () of the complex number. The polar form
is r
.
•Example 1:To  determine the absolute value (
r) and
argument () of 3+4i (Angle unit: Deg)
(r = 5,  = 53.13010235°)
(
r 
 5) A A R 3 + 4 i T =
( 
 53.13010235°)A a R 3 + 4 i T =
•The complex number can also...

E-10
BASE
•You select rectangular form (a+bi) or polar form (r
)
for display of complex number calculation results.
F...1(Disp) r
1
(a+bi): Rectangular form
2(r
): Polar form (indicated by “r
” on the display)
kConjugate of a Complex Number
For any complex number z where z = a+bi, its conjugate
(z) is z = a–bi.
•Example: To determine the conjugate of the complex
number 1.23 + 2.34
i  (Result: 1.23 – 2.34i)
A S R 1 l 23 + 2 l 34 i T =
A
 r
Base-n Calculations
Use the F key to enter the BASE Mode when...

E-11 •You can use the following logical operators between
values in Base-
n calculations: and (logical product), or
(logical sum), xor (exclusive or), xnor (exclusive nor),
Not (bitwise complement), and Neg (negation).
•The following are the allowable ranges for each of the
available number systems.
Binary 1000000000  
x 1111111111
0  x 0111111111
Octal 4000000000  x 7777777777
0  x 3777777777
Decimal –2147483648  x 2147483647
Hexadecimal 80000000  x FFFFFFFF
0  x 7FFFFFFF
• Example 1:To  p...

E-12
1    2    3     4
P (  Q (  R (  → t
SD
REG
SD
•Example 4:To  convert the value 2210 to its binary, oc-
tal, and hexadecimal equivalents.
(101102 , 268 , 1616 )
Binary mode:t b0.b
l l l 1(d) 22 =10110.b
Octal mode:o26.o
Hexadecimal mode:h16.H
•Example 5:To convert the value 51310 to its binary
equivalent.
Binary mode:
t b0.b
l l l 1(d) 513 =a MthERRORb
•You may not be able to convert a value from a number
system whose calculation range is greater than the cal-
culation range of the resulting number...

E-13
COMPDifferential
Calculations
The procedure described below obtains the derivative of
a function.
Use the 
F key to enter the COMP Mode when you
want to perform a calculation involving differentials.
COMP............................................................
F 1
•Three inputs are required for the differential expression:
the function of variable x, the point (a) at which the dif-
ferential coefficient is calculated, and the change in
x (∆x).A J expression P a P ∆x T
•Example: To determine the...

E-14
COMP
•You can omit input of ∆x, if you want. The calculator
automatically substitutes an appropriate value for ∆x if
you do not input one.
•Discontinuous points and extreme changes in the value
of x can cause inaccurate results and errors.
•Select Rad (Radian) for the angle unit setting when
performing trigonometric function differential calculations.
Integration
Calculations
The procedure described below obtains the definite integral
of a function.
Use the 
F key to enter the COMP Mode when you...

E-15
kCreating a Matrix
To create a matrix, press A
 j
 1(Dim), specify a matrix
name (A, B, or C), and then specify the dimensions
(number of rows and number of columns) of the matrix.
Next, follow the prompts that appear to input values that
make up the elements of the matrix.
You can use the cursor keys to move about the matrix in
order to view or edit its elements.
To exit the matrix screen, press 
t.
MATMatrix Calculations
The procedures in this section describe how to create
matrices with up to...

E-16
kEditing the Elements of a Matrix
Press A
 j
 2(Edit) and then specify the name (A, B, or
C) of the matrix you want to edit to display a screen for
editing the elements of the matrix.
kMatrix Addition, Subtraction, and
Multiplication
Use the procedures described below to add, subtract,
and multiply matrices.
•Example: To multiply Matrix A =                by
Matrix B =
(Matrix A 32)A
 j
 1(Dim)
 1(A)
 3 =
 2 =
(Element input)1 =
 2 =
 4 = 0 =
 D 2 =
 5 = t
(Matrix B 23)A
 j
 1(Dim)
 2(B)
 2 =
 3...

E-17
(Matrix C 2
2)A
 j 1
 (Dim)
 3(C)
 2 = 2 =
(Element input)2 =
 D 1 =
 D 5 = 3 = t
(3
MatC)3 -
 A
 j
 3(Mat)
 3(C)
 =
kObtaining the Determinant of a Matrix
You can use the procedure below to determine the
determinant of a square matrix.
•Example: To obtain the determinant of
Matrix A =                         (Result:
 73)
(Matrix A 3
3)A
 j
 1(Dim)
 1(A)
 3 = 3 =
(Element input)2 =
 D 1 = 6 = 5 = 0 = 1 =3 = 2 = 4 = t
(DetMatA)A
 j
 r
 1(Det)
A
 j
 3(Mat)
 1(A)
 =
•The above procedure results in an...

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VCT
0.4 1 0.8
1.5 0.5 1.5
0.8 0 0.6
[             ](                 )
kInverting a Matrix
You can use the procedure below to invert a square matrix.
•Example: To invert Matrix C =
(Matrix C 3
3)A
 j
 1(Dim)
 3(C)
 3 = 3 =
(Element input)D 3 = 6 =
 D 11  = 3 =
 D 4 =6 = 4 =
 D 8 = 13 = t
(MatC–1)A
 j
 3(Mat)
 3(C) a
 =
•  The above procedure results in an error if a non-square
matrix or a matrix for which there is no inverse
(determinant = 0) is specified.
kDetermining the Absolute Value of a...