#/***********************************************************
#    complex.rb -- 複素数
#***********************************************************/

class Complex
    def initialize(re, im)
        @re = re
        @im = im
    end

    attr_accessor :re, :im

    def to_s  # 複素数 $z = x + iy$ を文字列に変換 
        sprintf("%g%+gi", @re, @im)
    end

    def conj  # 共役複素数 $\overlinezend$ 
        Complex.new(@re, -@im)
    end

    def abs  # 絶対値 $|self|$ 
        if (@re == 0); return @im.abs; end
        if (@im == 0); return @re.abs; end
        if (@im.abs > @re.abs) 
            t = @re / @im
            return @im.abs * Math::sqrt(1 + t * t)
        else 
            t = @im / @re
            return @re.abs * Math::sqrt(1 + t * t)
        end
    end
    
    def arg  # 偏角 ($-\pi \le \varphi \le \pi$) 
        atan2(@im, @re)
    end
    
    def +(other)  # 和 $x + y$ 
        Complex.new(@re + other.re, @im + other.im)
    end
    
    def -(other)  # 差 $x - y$ 
        Complex.new(@re - other.re, @im - other.im)
    end
    
    def *(other)  # 積 $xy$ 
        Complex.new(@re * other.re - @im * other.im, @re * other.im + @im * other.re)
    end
    
=begin
    def /(other)  # 商 $x / y$ (単純版) 
        r2 = other.re * other.re + other.im * other.im
        re = (@re * other.re + @im * other.im) / r2.to_f
        im = (@im * other.re - @re * other.im) / r2.to_f
        Complex.new(re, im)
    end
=end
    
    def /(other)  # 商 $x / y$ (上位桁あふれ対策版) 
        if (other.re.abs >= other.im.abs) 
            w = other.im / other.re.to_f;  d = other.re + other.im * w
            re = (@re + @im * w) / d.to_f
            im = (@im - @re * w) / d.to_f
        else 
            w = other.re / other.im.to_f;  d = other.re * w + other.im
            re = (@re * w + @im) / d.to_f
            im = (@im * w - @re) / d.to_f
        end
        Complex.new(re, im)
    end
    
    def Complex.exp(x)  # 指数関数 $e^x$ 
        a = Math::exp(x.re)
        re = a * Math::cos(x.im)
        im = a * Math::sin(x.im)
        Complex.new(re, im)
    end
    
    def Complex.log(x)  # 自然対数 $\log_e x$ 
        re = 0.5 * Math::log(x.re * x.re + x.im * x.im)
        im = Math::atan2(x.im, x.re)
        Complex.new(re, im)
    end
    
    def **(other)  # 累乗 $x^y$ 
        Complex.exp(other * Complex.log(self))
    end
    
    def Complex.sin(x)  # 正弦 $\sin x$ 
        e = Math::exp(x.im);  f = 1 / e.to_f
        im = 0.5 * Math::cos(x.re) * (e - f)
        re = 0.5 * Math::sin(x.re) * (e + f)
        Complex.new(re, im)
    end
    
    def Complex.cos(x)  # 余弦 $\cos x$ 
        e = Math::exp(x.im);  f = 1 / e.to_f
        im = 0.5 * Math::sin(x.re) * (f - e)
        re = 0.5 * Math::cos(x.re) * (f + e)
        Complex.new(re, im)
    end
    
    def Complex.tan(x)  # 正接 $\tan x$ 
        e = Math::exp(2 * x.im);  f = 1 / e.to_f
        d = Math::cos(2 * x.re) + 0.5 * (e + f)
        re = Math::sin(2 * x.re) / d.to_f
        im = 0.5 * (e - f) / d.to_f
        Complex.new(re, im)
    end
    
    def Complex.sinh(x)  # 双曲線正弦 $\sinh x$ 
        e = Math::exp(x.re);  f = 1 / e
        re = 0.5 * (e - f) * Math::cos(x.im)
        im = 0.5 * (e + f) * Math::sin(x.im)
        Complex.new(re, im)
    end
    
    def Complex.cosh(x)  # 双曲線余弦 $\cosh x$ 
        e = Math::exp(x.re);  f = 1 / e.to_f
        re = 0.5 * (e + f) * Math::cos(x.im)
        im = 0.5 * (e - f) * Math::sin(x.im)
        Complex.new(re, im)
    end
    
    def Complex.tanh(x)  # 双曲線正接 $\tanh x$ 
        e = Math::exp(2 * x.re);  f = 1 / e.to_f
        d = 0.5 * (e + f) + Math::cos(2 * x.im)
        re = 0.5 * (e - f) / d.to_f
        im = Math::sin(2 * x.im) / d.to_f
        Complex.new(re, im)
    end
    
    SQRT05 = 0.707106781186547524
    
    def Complex.sqrt(x)  # 平方根 $\sqrtxend$ 
        r = x.abs
        w = Math::sqrt(r + x.re.abs)
        if (x.re >= 0) 
            re = SQRT05 * w
            im = SQRT05 * x.im / w.to_f
        else 
            re = SQRT05 * x.im.abs / w.to_f
            im = (x.im >= 0) ? SQRT05 * w : -SQRT05 * w
        end
        Complex.new(re, im)
    end
end

def c_conv(x, y)  # $x$, $y$ を複素数 $z = x + iy$ に変換 
    Complex.new(x, y)
end

printf("x, y ? ");  x, y = gets.scan(/[+-.\de]+/).collect{|x| x.to_f}
z = c_conv(x, y)
printf("z = %s\n", z.to_s)
z = Complex.exp(z)
printf("exp(z) = %s\n", z.to_s)
z = Complex.log(z)
printf("log(exp(z)) = %s\n", z.to_s)
printf("sqrt(z) * sqrt(z) = %s\n", Complex.sqrt(z) * Complex.sqrt(z))

exit 0