【C++】复数类的实现 |
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复数类的运算有加减乘除四个，下面我们来逐步分析这几个运算。 一·加法运算 设z1=a+bi,z2=c+di是任意两个复数，则它们的和是 (a+bi)+(c+di)=(a+c)+(b+d)i; 此处需要注意的是返回值的类型为复数complex。 二.减法运算 设z1=a+bi,z2=c+di是任意两个复数， 则它们的差是(a+bi)-(c+di)=(a-c)+(b-d)i. 同样这里的返回值类型也应该为复数complex。 三.乘法运算 设z1=a+bi，z2=c+di(a、b、c、d∈R)是任意两个复数，那么它们的积(a+bi)(c+di)=(ac-bd)+(bc+ad)i. 同样这里的返回值类型也应该为复数complex。 四.除法运算 满足(c+di)(x+yi)=(a+bi)的复数x+yi(x,y∈R)叫复数a+bi除以复数c+di的商 可以把 除法当成乘法做,分子分母上同时乘上分母的共轭.运算结果为： (ac+bd)/(c^2+d^2)+(bc-ad)/(c^2+d^2)i 同样这里的返回值类型也应该为复数complex。
具体代码实现如下： #include using namespace std; class Complex { public: Complex(double r,double i); Complex operator+(const Complex &c); Complex operator-(const Complex &c); Complex operator*(const Complex &c); Complex operator/(const Complex &c); Complex operator+=(const Complex &c); Complex operator-=(const Complex &c); bool operator==(const Complex &c); void print(Complex &c); private: double _real; double _image; }; Complex::Complex(double r = 0.0, double i = 0.0) { _real = r; _image = i; } //两复数相加 Complex Complex:: operator + (const Complex &c) { Complex tmp; tmp._real = _real + c._image; tmp._image = _image + c._image; return tmp; } //两复数相减 Complex Complex::operator - (const Complex &c) { Complex tmp; tmp._image = _image - c._image; tmp._real = _real - c._real; return tmp; } //两复数相乘(a+bi)(c+di)=(ac-bd)+(bc+ad)i Complex Complex::operator*(const Complex &c) { Complex tmp; tmp._real = _real*c._image - _image*c._real; tmp._image = _image*c._real + _real*c._image; return tmp; } //两复数相除(ac+bd)/(c^2+d^2)+(bc-ad)/(c^2+d^2)i Complex Complex :: operator/(const Complex &c) { Complex tmp; double deno = c._real*c._real + c._image*c._image;//有理化后的分母denominator tmp._real = deno*((_real*c._real) + (_image*c._image)); tmp._image = deno*((_image*c._real) - (_real*c._image)); return tmp; } Complex Complex::operator+=(const Complex &c) { Complex tmp; tmp._real += c._real; tmp._image += c._image; return tmp; } Complex Complex::operator-=(const Complex &c) { Complex tmp; tmp._real -= c._real; tmp._image -= c._image; return tmp; } bool Complex::operator==(const Complex &c) { return(_real == c._real) && (_image == c._image); } void Complex::print(Complex &c) { cout |
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