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@arki/math/complex

Immutable Complex with the same verbs as Decimal. Principal branches for sqrt, ln and pow; division by zero throws instead of giving NaN. toString() prints 3 + 4i and parses back exactly.

import { complex } from '@arki/math/complex';
 
complex(1, 1).pow(2).toString(); // '2i'
complex('3+4i').abs(); // 5
complex(-1).sqrt().toString(); // 'i'
complex(1).nthRoots(3).length; // 3
complex(1, 1).sin().toString(); // '1.2984575814159773 + 0.6349639147847361i'
complex(2).asin().toString(); // '1.5707963267948966 - 1.3169578969248166i'

sin, cos, tan, their inverses and the hyperbolic functions use principal branches (C99 Annex G). The library has no -0, so a point exactly on a branch cut takes Kahan's counter-clockwise rule, like sqrt and ln and like mpmath and Mathematica; C and NumPy pick the other side on half of the cuts. Measured within 3.1 ulp of a 700-digit reference from 1e-300 to 1e300.