Casio CFX-9850G PLUS User manual

Complex Numbers

This calculator is capable of performing the following operations

using complex numbers.

•Arithmetic operations (addition, subtraction, multiplication,

division)

•Calculation of the reciprocal, square root, and square of a

complex number

•Calculation of the absolute value and argument of a complex

number

•Calculation of conjugate complex numbers

•Extraction of the real part

•Extraction of the imaginary part

4-1 Before Beginning a Complex Number Calculation

4-2 Performing Complex Number Calculations

Chapter

4

68

4-1 Before Beginning a Complex Number

Calculation

Before beginning a complex number calculation, press K3(CPLX) to display

the complex number calculation menu.

•{i} ... {imaginary unit iinput}

•{Abs}/{Arg} ... obtains {absolute value}/{argument}

•{Conj} ... {obtains conjugate}

•{ReP}/{ImP} ... {real}/{imaginary} part extraction

69

4-2 Performing Complex Number Calculations

The following examples show how to perform each of the complex number

calculations available with this calculator.

kk

kk

kArithmetic Operations [OPTN]-[CPLX]-[i]

Arithmetic operations are the same as those you use for manual calculations. You

can even use parentheses and memory.

Example 1 (1 + 2i) + (2 + 3i)

AK3(CPLX)

(b+c1(i))

+(c+d1(i))w

Example 2 (2 + i) ×(2 – i)

AK3(CPLX)

(c+1(i))

*(c-1(i))w

kk

kk

kReciprocals, Square Roots, and Squares

Example (3 + i)

AK3(CPLX)

!9(d+1(i))w

kk

kk

kAbsolute Value and Argument [OPTN]-[CPLX]-[Abs]/[Arg]

The unit regards a complex number in the form a+ bi as a coordinate on a

Gaussian plane, and calculates absolute value Zand argument (arg).

Example To calculate absolute value (r) and argument (

θ

) for the

complex number 3 + 4i, with the angle unit set for degrees

Imaginary axis

Real axis

70

AK3(CPLX)2(Abs)

(d+e1(i))w

(Calculation of absolute value)

AK3(CPLX)3(Arg)

(d+e1(i))w

(Calculation of argument)

•The result of the argument calculation differs in accordance with the current

angle unit setting (degrees, radians, grads).

kk

kk

kConjugate Complex Numbers [OPTN]-[CPLX]-[Conj]

A complex number of the form a+ bi becomes a conjugate complex number of the

form a– bi.

Example To calculate the conjugate complex number for the complex

number 2 + 4i

AK3(CPLX)4(Conj)

(c+e1(i))w

kk

kk

kExtraction of Real and Imaginary Parts

[OPTN]-[CPLX]-[ReP]/[lmP]

Use the following procedure to extract the real part aand the imaginary part b

from a complex number of the form a+ bi.

Example To extract the real and imaginary parts of the complex number

2 + 5i

AK3(CPLX)5(ReP)

(c+f1(i))w

(Real part extraction)

AK3(CPLX)6(ImP)

(c+f1(i))w

(Imaginary part extraction)

4 - 2 Performing Complex Number Calculations

71

Performing Complex Number Calculations 4 - 2

kk

kk

kComplex Number Calculation Precautions

•The input/output range of complex numbers is normally 10 digits for the

mantissa and two digits for the exponent.

•When a complex number has more than 21 digits, the real part and imaginary

part are displayed on separate lines.

•When either the real part or imaginary part equals zero, that part is not

displayed.

•20 bytes of memory are used whenever you assign a complex number to a

variable.

•The following functions can be used with complex numbers.

, x2, x–1

← ←

Int, Frac, Rnd, Intg, Fix, Sci, ENG, ENG, °’ ”, °’ ”, ab/c, d/c, F⇔D

P. 2 2

72

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