I - Maple Help

I

root of x^2 = -1

Description

 • Maple uses I to represent one of the square roots of -1, with -I representing the other, for computations over the complex numbers.
 • Arithmetic expressions involving I and other numeric constants are automatically evaluated.
 • The evalc function can be used to symbolically manipulate complex-valued expressions.
 • The evalf function can be used to numerically evaluate complex-valued expressions.
 • The evalhf function can be used to numerically evaluate complex-valued expressions using the floating-point hardware of the underlying system.
 • I is implemented as Complex(1), and therefore, unlike many other Maple constants, type(I, name) returns false.
 • Since the literal expressions "sqrt(-1)" or "(-1)^(1/2)" do not appear in the representation of I, or any complex number in Maple, type(I, radical) returns false.
 • If you want to see this complex constant displayed as another letter (for example j), use interface(imaginaryunit=j).  See interface for  more information.

Examples

 > ${I}^{2}$
 ${-1}$ (1)
 > $\left(10+5I\right)\left(3+4I\right)$
 ${10}{+}{55}{}{I}$ (2)
 > $\mathrm{solutions}≔\mathrm{solve}\left({x}^{3}=-3\right)$
 ${\mathrm{solutions}}{≔}{-}{{3}}^{{1}}{{3}}}{,}\frac{{{3}}^{{1}}{{3}}}}{{2}}{-}\frac{{I}{}{{3}}^{{5}}{{6}}}}{{2}}{,}\frac{{{3}}^{{1}}{{3}}}}{{2}}{+}\frac{{I}{}{{3}}^{{5}}{{6}}}}{{2}}$ (3)
 > $\mathrm{evalf}\left(\left[\mathrm{solutions}\right]\right)$
 $\left[{-1.442249570}{,}{0.7211247850}{-}{1.249024766}{}{I}{,}{0.7211247850}{+}{1.249024766}{}{I}\right]$ (4)
 > $\mathrm{map}\left(\mathrm{evalhf},\left[\mathrm{solutions}\right]\right)$
 $\left[{-1.44224957030740830}{,}{0.721124785153704151}{-}{1.24902476648340643}{}{I}{,}{0.721124785153704151}{+}{1.24902476648340643}{}{I}\right]$ (5)