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ComplexBox

 Elementary
 elementary functions for ComplexBox objects
 Re
 compute the real part of a ComplexBox object
 Im
 compute the imaginary part of a ComplexBox object
 abs
 compute the absolute value of a ComplexBox object
 argument
 compute the argument of a ComplexBox object
 sqrt
 compute the square root of a ComplexBox object
 exp
 compute the exponential of a ComplexBox object
 log
 compute the logarithm of a ComplexBox object
 rsqrt
 compute the reciprocal square root of a ComplexBox object
 expm1
 compute the exponential of a ComplexBox object minus one
 expPiI
 compute the exponential of Pi*I times a ComplexBox object
 log1p
 compute the logarithm of a ComplexBox object minus one
 signum
 compute the signum of a ComplexBox object
 csgn
 compute the sign of a ComplexBox object

 Calling Sequence Re( b ) Im( b ) abs( b ) argument( b ) sqrt( b ) exp( b ) log( b ) rsqrt( b ) expm1( b ) expPiI( b ) log1p( b ) signum( b ) csgn( b )

Parameters

 b - ComplexBox object precopt - (optional) equation of the form precision = n, where n is a positive integer

Description

 • These are the standard basic elementary functions defined for ComplexBox objects.

 sqrt exp log abs argument signum csgn Re Im

 • They override the standard Maple procedures for ComplexBox objects.
 • Additionally, via "arblib", there are a number of variations that are not defined for standard numerics in Maple.

 rsqrt( b ) 1/sqrt( b ) expm1( b ) exp( b ) - 1 expPiI( b ) exp( Pi*b*I ) log1p( b ) log( 1 + b )

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

Examples

 > $b≔\mathrm{ComplexBox}\left(2.3+11.35I\right)$
 ${b}{≔}{⟨}{\text{ComplexBox:}}{\text{[2.3 +/- 2.32831e-10]}}{+}{\text{[11.35 +/- 9.31323e-10]}}{\cdot }{I}{⟩}$ (1)
 > $\mathrm{ℜ}\left(b\right)$
 ${⟨}{\text{RealBox:}}{2.3}{±}{2.32831ⅇ-10}{⟩}$ (2)
 > $\mathrm{ℑ}\left(b\right)$
 ${⟨}{\text{RealBox:}}{11.35}{±}{9.31323ⅇ-10}{⟩}$ (3)
 > $\left|b\right|$
 ${⟨}{\text{RealBox:}}{11.5807}{±}{1.97203ⅇ-09}{⟩}$ (4)
 > $\mathrm{argument}\left(b\right)$
 ${⟨}{\text{RealBox:}}{1.37086}{±}{1.7137ⅇ-10}{⟩}$ (5)
 > $\mathrm{signum}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.198606 +/- 8.5212e-11]}}{+}{\text{[0.980079 +/- 3.88106e-10]}}{\cdot }{I}{⟩}$ (6)
 > $\mathrm{csgn}\left(b\right)$
 ${⟨}{\text{RealBox:}}{1}{±}{0}{⟩}$ (7)
 > $\mathrm{csgn}\left(1,b\right)$
 ${⟨}{\text{RealBox:}}{0}{±}{0}{⟩}$ (8)

Note the exception raised in the following example, due to non-differentiability.

 > $\mathrm{csgn}\left(1,\mathrm{ComplexBox}\left(4.1I\right)\right)$
 > $\mathrm{csgn}\left(0,\mathrm{ComplexBox}\left(0\right),1\right)$
 ${⟨}{\text{RealBox:}}{1}{±}{0}{⟩}$ (9)
 > $\mathrm{csgn}\left(0,\mathrm{ComplexBox}\left(0\right),-1\right)$
 ${⟨}{\text{RealBox:}}{-1}{±}{0}{⟩}$ (10)
 > $b:-\mathrm{sqrt}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[2.63445 +/- 3.66495e-10]}}{+}{\text{[2.15415 +/- 5.18888e-10]}}{\cdot }{I}{⟩}$ (11)
 > $\mathrm{rsqrt}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.227487 +/- 6.46232e-11]}}{+}{\text{[-0.186012 +/- 5.43171e-11]}}{\cdot }{I}{⟩}$ (12)
 > ${ⅇ}^{b}$
 ${⟨}{\text{ComplexBox:}}{\text{[3.46156 +/- 1.05079e-08]}}{+}{\text{[-9.35425 +/- 7.86248e-09]}}{\cdot }{I}{⟩}$ (13)
 > $\mathrm{expm1}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[2.46156 +/- 9.94183e-09]}}{+}{\text{[-9.35425 +/- 6.5501e-09]}}{\cdot }{I}{⟩}$ (14)
 > $\mathrm{expPiI}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[1.92109e-16 +/- 1.79641e-24]}}{+}{\text{[2.64415e-16 +/- 2.33121e-24]}}{\cdot }{I}{⟩}$ (15)
 > $\mathrm{log}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[2.44934 +/- 3.15894e-10]}}{+}{\text{[1.37086 +/- 1.7137e-10]}}{\cdot }{I}{⟩}$ (16)
 > $\mathrm{log1p}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[2.46979 +/- 3.14239e-10]}}{+}{\text{[1.28785 +/- 1.75505e-10]}}{\cdot }{I}{⟩}$ (17)

Compatibility

 • The ComplexBox[Elementary], ComplexBox:-Re, ComplexBox:-Im, ComplexBox:-abs, ComplexBox:-argument, ComplexBox:-sqrt, ComplexBox:-exp, ComplexBox:-log, ComplexBox:-rsqrt, ComplexBox:-expm1, ComplexBox:-expPiI, ComplexBox:-log1p, ComplexBox:-signum and ComplexBox:-csgn commands were introduced in Maple 2022.