var Complex = function (arg0, arg1){
    arg0 = arg0 || 0;
    arg1 = arg1 || 0;
    if (typeof arg0 == "number" && typeof arg1 == "number"){
        this.r = arg0;
        this.i = arg1;
    } else {
        var tmp = Complex.conv(arg0)
        this.r = tmp.r;
        this.i = tmp.i;
    }
};

// 加減乗除メソッドは破壊的
Complex.prototype = {
    toString: function(){return Complex.toString(this);},
    valueOf:  function(){return Complex.toString(this);},
    abs: function(){return Complex.abs(this);},
    add: function(cn){
        var tmp = Complex.add(this, cn);
        this.r = tmp.r;
        this.i = tmp.i;
        return this;
    },
    sub: function(cn){
        var tmp = Complex.sub(this, cn);
        this.r = tmp.r;
        this.i = tmp.i;
        return this;
    },
    mul: function(cn){
        var tmp = Complex.mul(this, cn);
        this.r = tmp.r;
        this.i = tmp.i;
        return this;
    },
    div: function(cn){
        var tmp = Complex.div(this, cn);
        this.r = tmp.r;
        this.i = tmp.i;
        return this;
    }
};

// 以下はインスタンスのメソッドではない
// 引数をインスタンスもどき（メソッドなしでプロパティr, iのみのオブジェクト）に変換する関数
Complex.conv = function(arg){
    if (typeof arg == "object") {
        return {r: Number(arg.r || arg[0] || 0), i: Number(arg.i || arg[1] || 0)};
    } else if (typeof arg == "string") {
        var srcNum = "([+\\-]?(?:[0-9]+\\.?[0-9]*|0?\\.[0-9]+)(?:e[+\\-]?[0-9]+)?)";
        var reCNum = new RegExp("^(?:" + srcNum + "(?!i))?(?:" + srcNum + "i)?$", "i");
        reCNum.exec(arg.replace(/\s/g, "").replace(/(^|\+|-)i/i, "$11i"));
        return {r: Number(RegExp.$1), i: Number(RegExp.$2)};
    }
    return {r: Number(arg), i: 0};
};

// インスタンス相当を引数に取る関数
Complex.toString = function(cn){
    cn = Complex.conv(cn);
    return cn.r.toString() + (cn.i >= 0 ? "+" : "") + cn.i.toString() + "i";
};
Complex.abs = function(cn){
    cn = Complex.conv(cn);
    return Math.sqrt(cn.r * cn.r + cn.i * cn.i);
};
// 加減乗除関数は新しいインスタンスを返す
Complex.add = function(cn0, cn1){
    cn0 = Complex.conv(cn0);
    cn1 = Complex.conv(cn1);
    return new Complex(cn0.r + cn1.r, cn0.i + cn1.i);
};
Complex.sub = function(cn0, cn1){
    cn0 = Complex.conv(cn0);
    cn1 = Complex.conv(cn1);
    return new Complex(cn0.r - cn1.r, cn0.i - cn1.i);
};
Complex.mul = function(cn0, cn1){
    cn0 = Complex.conv(cn0);
    cn1 = Complex.conv(cn1);
    return new Complex(cn0.r * cn1.r - cn0.i * cn1.i,
                       cn0.i * cn1.r + cn0.r * cn1.i);
};
Complex.div = function(cn0, cn1){
    cn0 = Complex.conv(cn0);
    cn1 = Complex.conv(cn1);
    var absSq = cn1.r * cn1.r + cn1.i * cn1.i;
    return new Complex((cn0.r * cn1.r + cn0.i * cn1.i) / absSq,
                       (cn0.i * cn1.r - cn0.r * cn1.i) / absSq);
};
// 定義部はここまで

/* お題の計算。結果は以下
7+0i
3-15i
1+55i
1.1333333333333333-0.4i
3.605551275463989
*/
alert(
             Complex.add(new Complex(3, 1),  new Complex(4, -1))
    + "\n" + Complex.sub(new Complex(5, -9), new Complex(2, 6))
    + "\n" + Complex.mul(new Complex(5, 3),  new Complex(5, 8))
    + "\n" + Complex.div(new Complex(9, -7), new Complex(9, -3))
    + "\n" + Complex.abs(new Complex(2, 3))
);

// インスタンスを作る。引数は数値2つ、
// もしくは数値要素を2つ持つ（連想）配列か、複素数と解釈できる文字列
var c0 = new Complex(0, 1);
var c1 = new Complex([1, 1]);
var c2 = new Complex({r:3, i:-4});
var c3 = new Complex("5-8i");

// 絶対値を出してみる。上3行と下3行の結果は同じ。
alert(
             "|" + c0 + "| = " + Complex.abs(c0)
    + "\n" + "|" + c1 + "| = " + Complex.abs(c1)
    + "\n" + "|" + c2 + "| = " + Complex.abs(c2)
    + "\n" + "|" + c0 + "| = " + c0.abs()
    + "\n" + "|" + c1 + "| = " + c1.abs()
    + "\n" + "|" + c2 + "| = " + c2.abs()
);

// 計算1。引数なら文字列のままでも可。
// 下3行の計算は破壊的（c0の値が計算結果に変わる）
alert(
        "(" + c0 + ") + (" + c1   + ") = " + Complex.add(c0, c1)
    + "\n(" + c0 + ") - (" + c2   + ") = " + Complex.sub(c0, c2)
    + "\n(" + c0 + ") / (" + "-i" + ") = " + Complex.div(c0, "-i")
    + "\n(" + c0 + ") + (" + c1   + ") = " + c0.add(c1)
    + "\n(" + c0 + ") - (" + c2   + ") = " + c0.sub(c2)
    + "\n(" + c0 + ") / (" + "-i" + ") = " + c0.div("-i")
);

// 計算2。iの2乗。加減乗除の組み合わせ2つ。複素数を0で割ると0/0
alert(
      "i * i = " + Complex.mul("i", "i")

    + "\n(3+2i) * (5-i) * (-6+2i) / (5-i) / (-6+2i) = "
    + (new Complex("3+2i")).mul("5-i").mul("-6+2i").div("5-i").div("-6+2i")

    + "\n( (3+2i) + (4-i) ) * 2i * -.5i - (4-i) = "
    + Complex.add("3+2i", "4-i").mul("2i").mul("-.5i").sub("4-i")

    + "\n(1+2i) / 0 = " + Complex.div("1+2i", "0")
);

// 引数いろいろ。falsyな値や空配列は0+0iに
var testcases = [
    "-3-8i", "5", [0, 4], [2, -8],
    "-2+i", "-2-i", {r:-2.5, i:3e-2}, "-2E8 + I",
    "0", "i", Infinity, NaN, "", {}, null, undefined
];
for (var i = 0, rslt = ""; i < testcases.length; i++){
    rslt += (typeof testcases[i]) + ": " + testcases[i]
        + "\n\t\t" + (new Complex(testcases[i])) + "\n";
}
alert(rslt);