四则运算符（+、-、*、/、+=、-=、*=、/=）和关系运算符（>、<、<=、>=、==、!=）都是数学运算符，它们在实际开发中非常常见，被重载的几率也很高，并且有着相似的重载格式。本节以复数类 Complex 为例对它们进行重载，重在演示运算符重载的语法以及规范。

复数能够进行完整的四则运算，但不能进行完整的关系运算：我们只能判断两个复数是否相等，但不能比较它们的大小，所以不能对 >、<、<=、>= 进行重载。下面是具体的代码：

1. #include <iostream>

2. #include <cmath>

3. using namespace std;

4. //复数类

5. class Complex{

6. public:  //构造函数

7. Complex(double real = 0.0, double imag = 0.0): m_real(real), m_imag(imag){ }

8. public:  //运算符重载

9. //以全局函数的形式重载

10. friend Complex operator+(const Complex &c1, const Complex &c2);

11. friend Complex operator-(const Complex &c1, const Complex &c2);

12. friend Complex operator*(const Complex &c1, const Complex &c2);

13. friend Complex operator/(const Complex &c1, const Complex &c2);

14. friend bool operator==(const Complex &c1, const Complex &c2);

15. friend bool operator!=(const Complex &c1, const Complex &c2);

16. //以成员函数的形式重载

17. Complex & operator+=(const Complex &c);

18. Complex & operator-=(const Complex &c);

19. Complex & operator*=(const Complex &c);

20. Complex & operator/=(const Complex &c);

21. public:  //成员函数

22. double real() const{ return m_real; }

23. double imag() const{ return m_imag; }

24. private:

25. double m_real;  //实部

26. double m_imag;  //虚部

27. };

28. //重载+运算符

29. Complex operator+(const Complex &c1, const Complex &c2){

30. Complex c;

31. c.m_real = c1.m_real + c2.m_real;

32. c.m_imag = c1.m_imag + c2.m_imag;

33. return c;

34. }

35. //重载-运算符

36. Complex operator-(const Complex &c1, const Complex &c2){

37. Complex c;

38. c.m_real = c1.m_real - c2.m_real;

39. c.m_imag = c1.m_imag - c2.m_imag;

40. return c;

41. }

42. //重载*运算符  (a+bi) * (c+di) = (ac-bd) + (bc+ad)i

43. Complex operator*(const Complex &c1, const Complex &c2){

44. Complex c;

45. c.m_real = c1.m_real * c2.m_real - c1.m_imag * c2.m_imag;

46. c.m_imag = c1.m_imag * c2.m_real + c1.m_real * c2.m_imag;

47. return c;

48. }

49. //重载/运算符  (a+bi) / (c+di) = [(ac+bd) / (c²+d²)] + [(bc-ad) / (c²+d²)]i

50. Complex operator/(const Complex &c1, const Complex &c2){

51. Complex c;

52. c.m_real = (c1.m_real*c2.m_real + c1.m_imag*c2.m_imag) / (pow(c2.m_real, 2) + pow(c2.m_imag, 2));

53. c.m_imag = (c1.m_imag*c2.m_real - c1.m_real*c2.m_imag) / (pow(c2.m_real, 2) + pow(c2.m_imag, 2));

54. return c;

55. }

56. //重载==运算符

57. bool operator==(const Complex &c1, const Complex &c2){

58. if( c1.m_real == c2.m_real && c1.m_imag == c2.m_imag ){

59. return true;

60. }else{

61. return false;

62. }

63. }

64. //重载!=运算符

65. bool operator!=(const Complex &c1, const Complex &c2){

66. if( c1.m_real != c2.m_real || c1.m_imag != c2.m_imag ){

67. return true;

68. }else{

69. return false;

70. }

71. }

72. //重载+=运算符

73. Complex & Complex::operator+=(const Complex &c){

74. this->m_real += c.m_real;

75. this->m_imag += c.m_imag;

76. return *this;

77. }

78. //重载-=运算符

79. Complex & Complex::operator-=(const Complex &c){

80. this->m_real -= c.m_real;

81. this->m_imag -= c.m_imag;

82. return *this;

83. }

84. //重载*=运算符

85. Complex & Complex::operator*=(const Complex &c){

86. this->m_real = this->m_real * c.m_real - this->m_imag * c.m_imag;

87. this->m_imag = this->m_imag * c.m_real + this->m_real * c.m_imag;

88. return *this;

89. }

90. //重载/=运算符

91. Complex & Complex::operator/=(const Complex &c){

92. this->m_real = (this->m_real*c.m_real + this->m_imag*c.m_imag) / (pow(c.m_real, 2) + pow(c.m_imag, 2));

93. this->m_imag = (this->m_imag*c.m_real - this->m_real*c.m_imag) / (pow(c.m_real, 2) + pow(c.m_imag, 2));

94. return *this;

95. }

96. int main(){

97. Complex c1(25, 35);

98. Complex c2(10, 20);

99. Complex c3(1, 2);

100. Complex c4(4, 9);

101. Complex c5(34, 6);

102. Complex c6(80, 90);

103. Complex c7 = c1 + c2;

104. Complex c8 = c1 - c2;

105. Complex c9 = c1 * c2;

106. Complex c10 = c1 / c2;

107. cout<<"c7 = "<<c7.real()<<" + "<<c7.imag()<<"i"<<endl;

108. cout<<"c8 = "<<c8.real()<<" + "<<c8.imag()<<"i"<<endl;

109. cout<<"c9 = "<<c9.real()<<" + "<<c9.imag()<<"i"<<endl;

110. cout<<"c10 = "<<c10.real()<<" + "<<c10.imag()<<"i"<<endl;

111. c3 += c1;

112. c4 -= c2;

113. c5 *= c2;

114. c6 /= c2;

115. cout<<"c3 = "<<c3.real()<<" + "<<c3.imag()<<"i"<<endl;

116. cout<<"c4 = "<<c4.real()<<" + "<<c4.imag()<<"i"<<endl;

117. cout<<"c5 = "<<c5.real()<<" + "<<c5.imag()<<"i"<<endl;

118. cout<<"c6 = "<<c6.real()<<" + "<<c6.imag()<<"i"<<endl;

119. if(c1 == c2){

120. cout<<"c1 == c2"<<endl;

121. }

122. if(c1 != c2){

123. cout<<"c1 != c2"<<endl;

124. }

125. return 0;

126. }

运行结果：
c7 = 35 + 55i
c8 = 15 + 15i
c9 = -450 + 850i
c10 = 1.9 + -0.3i
c3 = 26 + 37i
c4 = -6 + -11i
c5 = 220 + 4460i
c6 = 5.2 + 1.592i
c1 != c2

需要注意的是，我们以全局函数的形式重载了 +、-、*、/、==、!=，以成员函数的形式重载了 +=、-=、*=、/=，而且应该坚持这样做，不能一股脑都写作成员函数或者全局函数。