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ComplexBox

Box objects in the complex plane

 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 );
 ${b}{≔}{⟨}{\text{ComplexBox:}}{\text{[2.3 +/- 2.32831e-10]}}{+}{\text{[4.1 +/- 4.65661e-10]}}{\cdot }{I}{⟩}$ (1)
 > type( b, ':-ComplexBox' );
 ${\mathrm{true}}$ (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' );
 ${\mathrm{true}}$ (3)
 > type( Im( b ), ':-RealBox' );
 ${\mathrm{true}}$ (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 ) );
 ${b}{≔}{⟨}{\text{ComplexBox:}}{\text{[2.3 +/- 2.32831e-10]}}{+}{\text{[7.77 +/- 4.65661e-10]}}{\cdot }{I}{⟩}$ (5)
 > type( b, ':-ComplexBox' );
 ${\mathrm{true}}$ (6)
 • The imaginary part is optional:
 > b := ComplexBox( RealBox( 2.3 ) );
 ${b}{≔}{⟨}{\text{ComplexBox:}}{\text{[2.3 +/- 2.32831e-10]}}{+}{\text{[0 +/- 0]}}{\cdot }{I}{⟩}$ (7)
 > type( b, ':-ComplexBox' );
 ${\mathrm{true}}$ (8)
 • The resulting Complexbox object has a zero imaginary part.
 > Im( b );
 ${⟨}{\text{RealBox:}}{0}{±}{0}{⟩}$ (9)
 • As for objects of type RealBox, a ComplexBox object is also of type BoxObject.
 > type( b, ':-BoxObject' );
 ${\mathrm{true}}$ (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 $0$, $1$, $I$, $\mathrm{\infty }+\mathrm{\infty }I$, and $\mathrm{undefined}+\mathrm{undefined}I$.
 • In additions, the symbolic constant $\mathrm{\pi }$ can be used and computed to high precision by using the precision= option.
 > ComplexBox( I );
 ${⟨}{\text{ComplexBox:}}{\text{[0 +/- 0]}}{+}{\text{[1 +/- 0]}}{\cdot }{I}{⟩}$ (11)
 > ComplexBox( Pi );
 ${⟨}{\text{ComplexBox:}}{\text{[3.14159 +/- 1.16415e-10]}}{+}{\text{[0 +/- 0]}}{\cdot }{I}{⟩}$ (12)
 > ComplexBox( Pi, 'precision' = 1000 );
 ${⟨}{\text{ComplexBox:}}{\text{[3.14159 +/- 1.86653e-301]}}{+}{\text{[0 +/- 0]}}{\cdot }{I}{⟩}$ (13)

Elementary Functions

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

Elementary

 compute the absolute value of a ComplexBox compute the argument of a ComplexBox compute the sign of a ComplexBox compute the exponential of a ComplexBox compute the exponential minus one of a ComplexBox compute the exponential of PiI times a ComplexBox compute the imaginary part of a ComplexBox compute the logarithm of a ComplexBox compute the logarithm of a ComplexBox minus one compute the real part of a ComplexBox compute the reciprocal square root of a ComplexBox compute the signum of a ComplexBox 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

 compute the inverse cosine of a ComplexBox compute the inverse cotangent of a ComplexBox compute the inverse cosecant of a ComplexBox compute the inverse secant of a ComplexBox compute the inverse sine of a ComplexBox compute the inverse tangent of a ComplexBox compute the cosine of a ComplexBox compute the cosine of a ComplexBox times Pi compute the cotangent of a ComplexBox compute the cotangent of a ComplexBox times Pi compute the cosecant of a ComplexBox compute the secant of a ComplexBox compute the sine of a ComplexBox compute the sinc of a ComplexBox compute the sinc of a ComplexBox times Pi compute the sine of a ComplexBox times Pi compute the tangent of a ComplexBox compute the tangent of a ComplexBox times Pi

Hyperbolic

 compute the inverse hyperbolic cosine of a ComplexBox compute the inverse hyperbolic sine of a ComplexBox compute the inverse hyperbolic tangent of a ComplexBox compute the hyperbolic cosine of a ComplexBox compute the hyperbolic cotangent of a ComplexBox compute the hyperbolic cosecant of a ComplexBox compute the hyperbolic secant of a ComplexBox compute the hyperbolic sine of a ComplexBox compute the hyperbolic sine and hyperbolic cosine of a ComplexBox compute the hyperbolic tangent of a ComplexBox

Special Functions

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

Special

 compute the Bessel I function of a ComplexBox compute the Bessel J function of a ComplexBox compute the Bessel K function of a ComplexBox compute the Bessel Y function of a ComplexBox compute the Chebyshev T function of a ComplexBox compute the Chebyshev U function of a ComplexBox compute the hyperbolic cosine integral of a ComplexBox compute the cosine integral of a ComplexBox compute the dilogarithm of a ComplexBox compute the exponential integral of a ComplexBox compute the GAMMA function of a ComplexBox compute the Hermite H function of a ComplexBox general hypergeometric function of a ComplexBox Kummer U function of a ComplexBox Legendre P function of a ComplexBox Legendre Q function of a ComplexBox compute the logarithmic integral of a ComplexBox compute the log-GAMMA function of a ComplexBox compute the digamma function of a ComplexBox compute the reciprocal GAMMA function of a ComplexBox compute the hyperbolic sine integral of a ComplexBox compute the sine integral of a ComplexBox compute the Riemann zeta function of a ComplexBox

Compatibility

 • The ComplexBox command was introduced in Maple 2022.