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ComplexBox

Box objects in the complex plane

Calling Sequence

Parameters

Description

Creating Complex Boxes

Special Values and Constants

Elementary Functions

Circular and Hyperbolic Functions

Special Functions

Compatibility

	Calling Sequence
	ComplexBox( re, im ) ComplexBox( re ) ComplexBox( z ) ComplexBox( b )

Parameters

re	-	RealBox object; the real part of the complex box
im	-	RealBox object; the imaginary part of the complex box
z	-	extended complex numeric value
b	-	ComplexBox object
precopt	-	(optional) equation of the form precision = n, where n is a positive integer

Description

•	A ComplexBox object represents a pair of RealBox objects comprising its real and complex parts.

Creating Complex Boxes

•	In this section we describe the construction of complex box objects.

•	The simplest way to create a ComplexBox object is to pass a complex number to the ComplexBox object constructor.

>	b := ComplexBox( 2.3 + 4.1*I );

$b ≔ ⟨ ComplexBox: [2.3 +/- 2.32831e-10] + [4.1 +/- 4.65661e-10] \cdot I ⟩$

(1)

>	type( b, ':-ComplexBox' );

$true$

(2)

•	The real and imaginary parts of the resulting ComplexBox object are of type RealBox. You can access them by calling the Re and Im methods.

>	type( Re( b ), ':-RealBox' );

$true$

(3)

>	type( Im( b ), ':-RealBox' );

$true$

(4)

•	The second way to create a ComplexBox object is to pass the RealBox objects for its real and imaginary parts.

>	b := ComplexBox( RealBox( 2.3 ), RealBox( 7.77 ) );

$b ≔ ⟨ ComplexBox: [2.3 +/- 2.32831e-10] + [7.77 +/- 4.65661e-10] \cdot I ⟩$

(5)

>	type( b, ':-ComplexBox' );

$true$

(6)

•	The imaginary part is optional:

>	b := ComplexBox( RealBox( 2.3 ) );

$b ≔ ⟨ ComplexBox: [2.3 +/- 2.32831e-10] + [0 +/- 0] \cdot I ⟩$

(7)

>	type( b, ':-ComplexBox' );

$true$

(8)

•	The resulting Complexbox object has a zero imaginary part.

Im( b );

$⟨ RealBox: 0 \pm 0 ⟩$

(9)

•	As for objects of type RealBox, a ComplexBox object is also of type BoxObject.

>	type( b, ':-BoxObject' );

$true$

(10)

•	Use the 'precision' = n option to control the precision used in these methods. For more details on precision, see BoxPrecision.

Special Values and Constants

•	The ComplexBox constructor recognizes several special values for which particular methods are invoked. These include the values $0$ , $1$ , $I$ , $\infty + \infty I$ , and $undefined + undefined I$ .

•	In additions, the symbolic constant $π$ can be used and computed to high precision by using the precision= option.

>	ComplexBox( I );

$⟨ ComplexBox: [0 +/- 0] + [1 +/- 0] \cdot I ⟩$

(11)

>	ComplexBox( Pi );

$⟨ ComplexBox: [3.14159 +/- 1.16415e-10] + [0 +/- 0] \cdot I ⟩$

(12)

>	ComplexBox( Pi, 'precision' = 1000 );

$⟨ ComplexBox: [3.14159 +/- 1.86653e-301] + [0 +/- 0] \cdot I ⟩$

(13)

Elementary Functions

•	The elementary functions that are available as methods for ComplexBox objects are listed as follows.

Elementary

abs	compute the absolute value of a ComplexBox
argument	compute the argument of a ComplexBox
csgn	compute the sign of a ComplexBox
exp	compute the exponential of a ComplexBox
expm1	compute the exponential minus one of a ComplexBox
expPiI	compute the exponential of PiI times a ComplexBox
Im	compute the imaginary part of a ComplexBox
log	compute the logarithm of a ComplexBox
log1p	compute the logarithm of a ComplexBox minus one
Re	compute the real part of a ComplexBox
rsqrt	compute the reciprocal square root of a ComplexBox
signum	compute the signum of a ComplexBox
sqrt	compute the square root of a ComplexBox

Circular and Hyperbolic Functions

•	Most of the standard circular and hyperbolic functions have been provided as ComplexBox object methods. Those defined are listed below.

Circular

arccos	compute the inverse cosine of a ComplexBox
arccot	compute the inverse cotangent of a ComplexBox
arccsc	compute the inverse cosecant of a ComplexBox
arcsec	compute the inverse secant of a ComplexBox
arcsin	compute the inverse sine of a ComplexBox
arctan	compute the inverse tangent of a ComplexBox
cos	compute the cosine of a ComplexBox
cospi	compute the cosine of a ComplexBox times Pi
cot	compute the cotangent of a ComplexBox
cotpi	compute the cotangent of a ComplexBox times Pi
csc	compute the cosecant of a ComplexBox
sec	compute the secant of a ComplexBox
sin	compute the sine of a ComplexBox
sinc	compute the sinc of a ComplexBox
sincpi	compute the sinc of a ComplexBox times Pi
sinpi	compute the sine of a ComplexBox times Pi
tan	compute the tangent of a ComplexBox
tanpi	compute the tangent of a ComplexBox times Pi

Hyperbolic

arccosh	compute the inverse hyperbolic cosine of a ComplexBox
arcsinh	compute the inverse hyperbolic sine of a ComplexBox
arctanh	compute the inverse hyperbolic tangent of a ComplexBox
cosh	compute the hyperbolic cosine of a ComplexBox
coth	compute the hyperbolic cotangent of a ComplexBox
csch	compute the hyperbolic cosecant of a ComplexBox
sech	compute the hyperbolic secant of a ComplexBox
sinh	compute the hyperbolic sine of a ComplexBox
sinhcosh	compute the hyperbolic sine and hyperbolic cosine of a ComplexBox
tanh	compute the hyperbolic tangent of a ComplexBox

Special Functions

•	Many special and hypergeometric functions are available as ComplexBox object methods, as listed here:

Special

BesselI	compute the Bessel I function of a ComplexBox
BesselJ	compute the Bessel J function of a ComplexBox
BesselK	compute the Bessel K function of a ComplexBox
BesselY	compute the Bessel Y function of a ComplexBox
ChebyshevT	compute the Chebyshev T function of a ComplexBox
ChebyshevU	compute the Chebyshev U function of a ComplexBox
Chi	compute the hyperbolic cosine integral of a ComplexBox
Ci	compute the cosine integral of a ComplexBox
dilog	compute the dilogarithm of a ComplexBox
Ei	compute the exponential integral of a ComplexBox
GAMMA	compute the GAMMA function of a ComplexBox
HermiteH	compute the Hermite H function of a ComplexBox
hypergeom	general hypergeometric function of a ComplexBox
KummerU	Kummer U function of a ComplexBox
LegendreP	Legendre P function of a ComplexBox
LegendreQ	Legendre Q function of a ComplexBox
Li	compute the logarithmic integral of a ComplexBox
lnGAMMA	compute the log-GAMMA function of a ComplexBox
Psi	compute the digamma function of a ComplexBox
rGAMMA	compute the reciprocal GAMMA function of a ComplexBox
Shi	compute the hyperbolic sine integral of a ComplexBox
Si	compute the sine integral of a ComplexBox
Zeta	compute the Riemann zeta function of a ComplexBox

Compatibility

•	The ComplexBox command was introduced in Maple 2022.

•	For more information on Maple 2022 changes, see Updates in Maple 2022.

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Product Training

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