The arithmetic operators $\mathrm{`+`}$, $\mathrm{`*`}$, $\mathrm{`^`}$, $\mathrm{`-`}$ and $\mathrm{`/`}$ are available as methods for ComplexBox objects.

Addition (+) and multiplication (*) are $n$-ary operators that support more than two operands. The operators of negation (-) and inversion (/) are unary. The non-associative exponentiation operator (^) is binary.

The conjugate of a ComplexBox object b can be computed by using the conjugate( b ) command.

To compute roots of a ComplexBox object b, use the root( b, n ) command.

$-\mathrm{ComplexBox}\left(2.3+5.7\mathrm{I}\right)$

$⟨\text{ComplexBox:}\text{[-2.3 +/- 2.32831e-10]}+\text{[-5.7 +/- 4.65661e-10]}\cdot \mathrm{I}⟩$

$\mathrm{ComplexBox}\left(2.3+5.7\mathrm{I}\right)+\mathrm{ComplexBox}\left(1.1-0.321\mathrm{I}\right)$

$⟨\text{ComplexBox:}\text{[3.4 +/- 5.82077e-10]}+\text{[5.379 +/- 4.94765e-10]}\cdot \mathrm{I}⟩$

$\mathrm{ComplexBox}\left(2.3+5.7\mathrm{I}\right)-\mathrm{ComplexBox}\left(1.1-0.321\mathrm{I}\right)$

$⟨\text{ComplexBox:}\text{[1.2 +/- 3.49246e-10]}+\text{[6.021 +/- 4.94765e-10]}\cdot \mathrm{I}⟩$

$\mathrm{ComplexBox}\left(2.3+5.7\mathrm{I}\right)\mathrm{ComplexBox}\left(1.1-0.321\mathrm{I}\right)$

$⟨\text{ComplexBox:}\text{[4.3597 +/- 1.3049e-09]}+\text{[5.5317 +/- 1.78313e-09]}\cdot \mathrm{I}⟩$

$\frac{\mathrm{ComplexBox}\left(2.3+5.7\mathrm{I}\right)}{\mathrm{ComplexBox}\left(1.1-0.321\mathrm{I}\right)}$

$⟨\text{ComplexBox:}\text{[0.533342 +/- 1.40432e-09]}+\text{[5.33746 +/- 2.33351e-09]}\cdot \mathrm{I}⟩$

${\mathrm{ComplexBox}\left(2.3+5.7\mathrm{I}\right)}^{\mathrm{ComplexBox}\left(1.1-0.321\mathrm{I}\right)}$

$⟨\text{ComplexBox:}\text{[8.0897 +/- 1.24388e-08]}+\text{[7.13964 +/- 1.16935e-08]}\cdot \mathrm{I}⟩$

$\mathrm{conjugate}\left(\mathrm{ComplexBox}\left(2.3+5.7\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[2.3 +/- 2.32831e-10]}+\text{[-5.7 +/- 4.65661e-10]}\cdot \mathrm{I}⟩$

$p≔2x$

$p≔2x$

$\mathrm{eval}\left(p\,x=\mathrm{ComplexBox}\left(2.3+5.7\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[4.6 +/- 4.65661e-10]}+\text{[11.4 +/- 9.31323e-10]}\cdot \mathrm{I}⟩$

$p≔2x^2$

$p≔2x^2$

$\mathrm{eval}\left(p\,x=\mathrm{ComplexBox}\left(2.3+5.7\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[-54.4 +/- 1.64844e-08]}+\text{[52.44 +/- 1.33179e-08]}\cdot \mathrm{I}⟩$

$p≔2x^2-x$

$p≔2x^2-x$

$\mathrm{eval}\left(p\,x=\mathrm{ComplexBox}\left(2.3+5.7\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[-56.7 +/- 2.04425e-08]}+\text{[46.74 +/- 1.75089e-08]}\cdot \mathrm{I}⟩$

$p≔2x^2-3x$

$p≔2x^2-3x$

$\mathrm{eval}\left(p\,x=\mathrm{ComplexBox}\left(2.3+5.7\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[-61.3 +/- 2.13739e-08]}+\text{[35.34 +/- 2.03028e-08]}\cdot \mathrm{I}⟩$

$p≔\mathrm{randpoly}\left(x\right)\:$

$\mathrm{eval}\left(p\,x=\mathrm{ComplexBox}\left(2.3+5.7\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[-42241.5 +/- 9.30244e-05]}+\text{[-7262.81 +/- 6.90875e-05]}\cdot \mathrm{I}⟩$

$q≔\mathrm{randpoly}\left(\left[x\,y\right]\,'\mathrm{degree}'=30\,'\mathrm{dense}'\right)\:$

$\mathrm{eval}\left(\frac{p^3}{q}\,\left[x=\mathrm{ComplexBox}\left(1.1-0.321\mathrm{I}\right)\,y=\mathrm{ComplexBox}\left(2.3+5.7\mathrm{I}\right)\right]\right)$

$⟨\text{ComplexBox:}\text{[7.65384e-20 +/- 6.73062e-27]}+\text{[1.23419e-20 +/- 6.81317e-27]}\cdot \mathrm{I}⟩$

$\mathrm{root}\left(\mathrm{ComplexBox}\left(2.3+5.7\mathrm{I}\right)\,2\right)$

$⟨\text{ComplexBox:}\text{[2.05506 +/- 1.09856e-10]}+\text{[1.38682 +/- 3.03849e-10]}\cdot \mathrm{I}⟩$

$\mathrm{root}\left(\mathrm{ComplexBox}\left(2.3+5.7\mathrm{I}\right)\,3\right)$

$⟨\text{ComplexBox:}\text{[1.69021 +/- 4.06526e-10]}+\text{[0.706168 +/- 2.22582e-10]}\cdot \mathrm{I}⟩$

$\mathrm{root}\left(\mathrm{ComplexBox}\left(2.3+5.7\mathrm{I}\right)\,10\right)$

$⟨\text{ComplexBox:}\text{[1.19068 +/- 3.15463e-10]}+\text{[0.142034 +/- 4.78971e-11]}\cdot \mathrm{I}⟩$

The ComplexBox[Arithmetic], ComplexBox:-+, ComplexBox:-*, ComplexBox:-^, ComplexBox:--, ComplexBox:-/, ComplexBox:-conjugate and ComplexBox:-root commands were introduced in Maple 2022.

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