/*
Complex.js v2.4.3 11/13/2025
https://raw.org/article/complex-numbers-in-javascript/

Copyright (c) 2025, Robert Eisele (https://raw.org/)
Licensed under the MIT license.
*/
'use strict';(function(q){function l(a,b){if(a===void 0||a===null)f.re=f.im=0;else if(b!==void 0)f.re=a,f.im=b;else switch(typeof a){case "object":if("im"in a&&"re"in a)f.re=a.re,f.im=a.im;else if("abs"in a&&"arg"in a){if(!isFinite(a.abs)&&isFinite(a.arg))return c.INFINITY;f.re=a.abs*Math.cos(a.arg);f.im=a.abs*Math.sin(a.arg)}else if("r"in a&&"phi"in a){if(!isFinite(a.r)&&isFinite(a.phi))return c.INFINITY;f.re=a.r*Math.cos(a.phi);f.im=a.r*Math.sin(a.phi)}else a.length===2?(f.re=a[0],f.im=a[1]):m();
break;case "string":f.im=f.re=0;a=a.replace(/_/g,"").match(/\d+\.?\d*e[+-]?\d+|\d+\.?\d*|\.\d+|./g);b=1;let d=0;a===null&&m();for(let e=0;e<a.length;e++){const g=a[e];g!==" "&&g!=="\t"&&g!=="\n"&&(g==="+"?b++:g==="-"?d++:(g==="i"||g==="I"?(b+d===0&&m(),a[e+1]===" "||isNaN(a[e+1])?f.im+=parseFloat((d%2?"-":"")+"1"):(f.im+=parseFloat((d%2?"-":"")+a[e+1]),e++)):((b+d===0||isNaN(g))&&m(),a[e+1]==="i"||a[e+1]==="I"?(f.im+=parseFloat((d%2?"-":"")+g),e++):f.re+=parseFloat((d%2?"-":"")+g)),b=d=0))}b+d>0&&
m();break;case "number":f.im=0;f.re=a;break;default:m()}return f}function m(){throw SyntaxError("Invalid Param");}function n(a,b){a=Math.abs(a);b=Math.abs(b);a<b&&([a,b]=[b,a]);if(a<1E8)return Math.sqrt(a*a+b*b);b/=a;return a*Math.sqrt(1+b*b)}function p(a,b){const d=Math.abs(a),e=Math.abs(b);if(a===0)return Math.log(e);if(b===0)return Math.log(d);if(d<3E3&&e<3E3)return Math.log(a*a+b*b)*.5;a*=.5;b*=.5;return.5*Math.log(a*a+b*b)+Math.LN2}function c(a,b){if(!(this instanceof c))return new c(a,b);a=
l(a,b);this.re=a.re;this.im=a.im}const h=Math.cosh||function(a){return Math.abs(a)<1E-9?1-a:(Math.exp(a)+Math.exp(-a))*.5},k=Math.sinh||function(a){return Math.abs(a)<1E-9?a:(Math.exp(a)-Math.exp(-a))*.5},f={re:0,im:0};c.prototype={re:0,im:0,sign:function(){const a=n(this.re,this.im);return new c(this.re/a,this.im/a)},add:function(a,b){a=l(a,b);b=this.isInfinite();const d=!(isFinite(a.re)&&isFinite(a.im));return b||d?b&&d?c.NAN:c.INFINITY:new c(this.re+a.re,this.im+a.im)},sub:function(a,b){a=l(a,
b);b=this.isInfinite();const d=!(isFinite(a.re)&&isFinite(a.im));return b||d?b&&d?c.NAN:c.INFINITY:new c(this.re-a.re,this.im-a.im)},mul:function(a,b){a=l(a,b);b=this.isInfinite();const d=!(isFinite(a.re)&&isFinite(a.im)),e=this.re===0&&this.im===0,g=a.re===0&&a.im===0;return b&&g||d&&e?c.NAN:b||d?c.INFINITY:a.im===0&&this.im===0?new c(this.re*a.re,0):new c(this.re*a.re-this.im*a.im,this.re*a.im+this.im*a.re)},div:function(a,b){a=l(a,b);b=this.isInfinite();const d=!(isFinite(a.re)&&isFinite(a.im)),
e=this.re===0&&this.im===0,g=a.re===0&&a.im===0;if(e&&g||b&&d)return c.NAN;if(g||b)return c.INFINITY;if(e||d)return c.ZERO;if(0===a.im)return new c(this.re/a.re,this.im/a.re);if(Math.abs(a.re)<Math.abs(a.im))return b=a.re/a.im,a=a.re*b+a.im,new c((this.re*b+this.im)/a,(this.im*b-this.re)/a);b=a.im/a.re;a=a.im*b+a.re;return new c((this.re+this.im*b)/a,(this.im-this.re*b)/a)},pow:function(a,b){a=l(a,b);b=this.re===0&&this.im===0;if(a.re===0&&a.im===0)return c.ONE;if(a.im===0){if(this.im===0&&this.re>
0)return new c(Math.pow(this.re,a.re),0);if(this.re===0)switch((a.re%4+4)%4){case 0:return new c(Math.pow(this.im,a.re),0);case 1:return new c(0,Math.pow(this.im,a.re));case 2:return new c(-Math.pow(this.im,a.re),0);case 3:return new c(0,-Math.pow(this.im,a.re))}}if(b&&a.re>0)return c.ZERO;const d=Math.atan2(this.im,this.re),e=p(this.re,this.im);b=Math.exp(a.re*e-a.im*d);a=a.im*e+a.re*d;return new c(b*Math.cos(a),b*Math.sin(a))},sqrt:function(){const a=this.re,b=this.im;if(b===0)return a>=0?new c(Math.sqrt(a),
0):new c(0,Math.sqrt(-a));var d=n(a,b);d=Math.sqrt(.5*(d+Math.abs(a)));let e=Math.abs(b)/(2*d);return a>=0?new c(d,b<0?-e:e):new c(e,b<0?-d:d)},exp:function(){const a=Math.exp(this.re);return this.im===0?new c(a,0):new c(a*Math.cos(this.im),a*Math.sin(this.im))},expm1:function(){const a=this.re,b=this.im,d=Math.sin(.5*b);return new c(Math.expm1(a)*Math.cos(b)+-2*d*d,Math.exp(a)*Math.sin(b))},log:function(){const a=this.re,b=this.im;return b===0&&a>0?new c(Math.log(a),0):new c(p(a,b),Math.atan2(b,
a))},abs:function(){return n(this.re,this.im)},arg:function(){return Math.atan2(this.im,this.re)},sin:function(){const a=this.re,b=this.im;return new c(Math.sin(a)*h(b),Math.cos(a)*k(b))},cos:function(){const a=this.re,b=this.im;return new c(Math.cos(a)*h(b),-Math.sin(a)*k(b))},tan:function(){const a=2*this.re,b=2*this.im,d=Math.cos(a)+h(b);return new c(Math.sin(a)/d,k(b)/d)},cot:function(){const a=2*this.re,b=2*this.im,d=Math.cos(a)-h(b);return new c(-Math.sin(a)/d,k(b)/d)},sec:function(){const a=
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a.re)},atan:function(){var a=this.re;const b=this.im;if(a===0){if(b===1)return new c(0,Infinity);if(b===-1)return new c(0,-Infinity)}const d=a*a+(1-b)*(1-b);a=(new c((1-b*b-a*a)/d,-2*a/d)).log();return new c(-.5*a.im,.5*a.re)},acot:function(){const a=this.re,b=this.im;if(b===0)return new c(Math.atan2(1,a),0);const d=a*a+b*b;return d!==0?(new c(a/d,-b/d)).atan():(new c(a!==0?a/0:0,b!==0?-b/0:0)).atan()},asec:function(){const a=this.re,b=this.im;if(a===0&&b===0)return new c(0,Infinity);const d=a*a+
b*b;return d!==0?(new c(a/d,-b/d)).acos():(new c(a!==0?a/0:0,b!==0?-b/0:0)).acos()},acsc:function(){const a=this.re,b=this.im;if(a===0&&b===0)return new c(Math.PI/2,Infinity);const d=a*a+b*b;return d!==0?(new c(a/d,-b/d)).asin():(new c(a!==0?a/0:0,b!==0?-b/0:0)).asin()},sinh:function(){const a=this.re,b=this.im;return new c(k(a)*Math.cos(b),h(a)*Math.sin(b))},cosh:function(){const a=this.re,b=this.im;return new c(h(a)*Math.cos(b),k(a)*Math.sin(b))},tanh:function(){const a=2*this.re,b=2*this.im,d=
h(a)+Math.cos(b);return new c(k(a)/d,Math.sin(b)/d)},coth:function(){const a=2*this.re,b=2*this.im,d=h(a)-Math.cos(b);return new c(k(a)/d,-Math.sin(b)/d)},csch:function(){const a=this.re,b=this.im,d=Math.cos(2*b)-h(2*a);return new c(-2*k(a)*Math.cos(b)/d,2*h(a)*Math.sin(b)/d)},sech:function(){const a=this.re,b=this.im,d=Math.cos(2*b)+h(2*a);return new c(2*h(a)*Math.cos(b)/d,-2*k(a)*Math.sin(b)/d)},asinh:function(){const a=this.re;var b=this.im;if(b===0){if(a===0)return new c(0,0);b=Math.abs(a);b=
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0):a===1?new c(Infinity,0):a===-1?new c(-Infinity,0):-1<a&&a<1?new c(.5*Math.log((1+a)/(1-a)),0):a>1?new c(.5*Math.log((a+1)/(a-1)),-Math.PI/2):new c(.5*Math.log(-((1+a)/(1-a))),Math.PI/2);const d=1-a,e=1+a,g=d*d+b*b;if(g===0)return new c(a!==-1?a/0:0,b!==0?b/0:0);a=(e*d-b*b)/g;b=(b*d+e*b)/g;return new c(p(a,b)/2,Math.atan2(b,a)/2)},acoth:function(){const a=this.re,b=this.im;if(a===0&&b===0)return new c(0,Math.PI/2);const d=a*a+b*b;return d!==0?(new c(a/d,-b/d)).atanh():(new c(a!==0?a/0:0,b!==0?-b/
0:0)).atanh()},acsch:function(){var a=this.re;const b=this.im;if(b===0){if(a===0)return new c(Infinity,0);a=1/a;return new c(Math.log(a+Math.sqrt(a*a+1)),0)}const d=a*a+b*b;return d!==0?(new c(a/d,-b/d)).asinh():(new c(a!==0?a/0:0,b!==0?-b/0:0)).asinh()},asech:function(){const a=this.re,b=this.im;if(this.isZero())return c.INFINITY;const d=a*a+b*b;return d!==0?(new c(a/d,-b/d)).acosh():(new c(a!==0?a/0:0,b!==0?-b/0:0)).acosh()},inverse:function(){if(this.isZero())return c.INFINITY;if(this.isInfinite())return c.ZERO;
const a=this.re,b=this.im,d=a*a+b*b;return new c(a/d,-b/d)},conjugate:function(){return new c(this.re,-this.im)},neg:function(){return new c(-this.re,-this.im)},ceil:function(a){a=Math.pow(10,a||0);return new c(Math.ceil(this.re*a)/a,Math.ceil(this.im*a)/a)},floor:function(a){a=Math.pow(10,a||0);return new c(Math.floor(this.re*a)/a,Math.floor(this.im*a)/a)},round:function(a){a=Math.pow(10,a||0);return new c(Math.round(this.re*a)/a,Math.round(this.im*a)/a)},equals:function(a,b){a=l(a,b);return Math.abs(a.re-
this.re)<=c.EPSILON&&Math.abs(a.im-this.im)<=c.EPSILON},clone:function(){return new c(this.re,this.im)},toString:function(){let a=this.re,b=this.im,d="";if(this.isNaN())return"NaN";if(this.isInfinite())return"Infinity";Math.abs(a)<c.EPSILON&&(a=0);Math.abs(b)<c.EPSILON&&(b=0);if(b===0)return d+a;a!==0?(d=d+a+" ",b<0?(b=-b,d+="-"):d+="+",d+=" "):b<0&&(b=-b,d+="-");1!==b&&(d+=b);return d+"i"},toVector:function(){return[this.re,this.im]},valueOf:function(){return this.im===0?this.re:null},isNaN:function(){return isNaN(this.re)||
isNaN(this.im)},isZero:function(){return this.im===0&&this.re===0},isFinite:function(){return isFinite(this.re)&&isFinite(this.im)},isInfinite:function(){return!this.isFinite()}};c.ZERO=new c(0,0);c.ONE=new c(1,0);c.I=new c(0,1);c.PI=new c(Math.PI,0);c.E=new c(Math.E,0);c.INFINITY=new c(Infinity,Infinity);c.NAN=new c(NaN,NaN);c.EPSILON=1E-15;typeof define==="function"&&define.amd?define([],function(){return c}):typeof exports==="object"?(Object.defineProperty(c,"__esModule",{value:!0}),c["default"]=
c,c.Complex=c,module.exports=c):q.Complex=c})(this);