我们先创建一个有利于后续操作的头文件，把预处理命令和一些常用的的宏(之后会用到)封装在头文件"StdFile.h"里面。
以下为"StdFile.h"里面的信息:
#include#include#include#include#define _USE_MATH_DEFINES
#include#includeusing namespace std;
#define OK 1
#define ERROR 0
#define TRUE 1
#define FALSE 0
typedef long long ElemType;
typedef int Index;
typedef int Num;
typedef int Step; 之后对复数的基本定义:
typedef struct
{
Real real;
Imag imag;
}Complex;
再创建一个头文件"Complex.h"，里面存放关于复数的一些基本方法。
以下为"Complex.h"里面的信息:
#include "StdFile.h"
typedef long double Real, Imag;
typedef long double RealNum;
typedef struct
{
Real real;
Imag imag;
}Complex;
//创建复数
Complex CreateComplex(Real x = 0, Imag y = 0)
{
Complex z = { 0,0 };
z.real = x;
z.imag = y;
return z;
}
//打印复数
void PrintComplex(Complex z)
{
if (z.real == 0)
printf("j%.2llf\n", z.imag);
else
printf("%.2llf+j%.2llf\n", z.real, z.imag);
}
//获取实部
RealNum RealComplex(Complex z)
{
return z.real;
}
//获取虚部
RealNum ImagComplex(Complex z)
{
return z.imag;
}
//共轭复数
Complex ConjugateComplex(Complex z)
{
Complex _z;
_z.real = z.real;
_z.imag = -z.imag;
return _z;
}
//复数的模
RealNum AbsComplex(Complex z)
{
RealNum r = 0;
r = sqrt(z.real * z.real + z.imag * z.imag);
return r;
}
//复数加法
Complex AddComplex(Complex z1, Complex z2)
{
Complex z3 = { 0,0 };
z3.real = z1.real + z2.real;
z3.imag = z1.imag + z2.imag;
return z3;
}
//复数减法
Complex SubComplex(Complex z1, Complex z2)
{
Complex z3 = { 0,0 };
z3.real = z1.real - z2.real;
z3.imag = z1.imag - z1.imag;
return z3;
}
//复数乘法
Complex MulComplex(Complex z1, Complex z2)
{
Complex z3 = { 0,0 };
z3.real = z1.real * z2.real - z1.imag * z2.imag;
z3.imag = z1.real * z2.imag + z1.imag * z2.real;
return z3;
}
//复数除法
Complex DivComplex(Complex z1, Complex z2)
{
Complex z3 = { 0,0 };
z3.real = (z1.real * z2.real + z1.imag * z2.imag) / (z2.real * z2.real + z2.imag * z2.imag);
z3.imag = (z1.imag * z2.real - z1.real * z2.imag) / (z2.real * z2.real + z2.imag * z2.imag);
return z3;
}
//复数的辐角
RealNum ArgComplex(Complex z)
{
RealNum r;
if (z.real >= 0 && z.imag == 0)
r = 0;
else if (z.real< 0 && z.imag == 0)
r = M_PI;
else if (z.real >= 0)
r = atan(z.imag / z.real);
else if (z.real< 0 && z.imag>0)
r = atan(z.imag / z.real) + M_PI;
else
r = atan(z.imag / z.real) - M_PI;
return r;
}此方法不全，读者可添加更多方法(比如复数的三角式，复数的指数式，复数的幂，复数的对数，指数……）
以下为效果展示:
#include "Complex.h"
int main()
{
Complex Z1, Z2, Z;
Z = { 6,8 };
Z1 = { 1,0 };
Z2 = CreateComplex(2, 4);
PrintComplex(Z1);
PrintComplex(Z2);
PrintComplex(AddComplex(Z1, Z2));
cout<< "Z1+Z2的模 "<< AbsComplex(AddComplex(Z1, Z2))<< endl;
cout<< "Z的实部 "<< RealComplex(Z)<< ' '<< "Z的虚部"<< ImagComplex(Z)<< endl;
cout<< "打印Z/(Z1+Z2) ";
PrintComplex(DivComplex(Z, AddComplex(Z1, Z2)));
cout<< "Z的辐角主值 "<< ArgComplex(Z)<< endl;
}显示结果:
辐角主值以弧度制显示，可能很难看出角度，优化后可以把弧度转化为角度：
//复数的辐角
RealNum ArgComplex(Complex z)
{
RealNum r;
if (z.real >= 0 && z.imag == 0)
r = 0;
else if (z.real< 0 && z.imag == 0)
r = M_PI;
else if (z.real >= 0)
r = atan(z.imag / z.real);
else if (z.real< 0 && z.imag>0)
r = atan(z.imag / z.real) + M_PI;
else
r = atan(z.imag / z.real) - M_PI;
return r/M_PI*180;
}只需修改返回值即可。
修改后主函数的运行结果:
arctan(8/6)刚好就是53.1°，辐角显示无误。
以下是资源文件里面的文本文件"Help.Complex.txt"的内容，为方法的使用大纲:
typedef struct
{
Real real;
Imag imag;
}Complex;
//创建复数
Complex CreateComplex(Real x = 0, Imag y = 0)
//打印复数
void PrintComplex(Complex z)
//获取实部
RealNum RealComplex(Complex z)
//获取虚部
RealNum ImagComplex(Complex z)
//共轭复数
Complex ConjugateComplex(Complex z)
//复数的模
RealNum AbsComplex(Complex z)
//复数加法
Complex AddComplex(Complex z1, Complex z2)
//复数减法
Complex SubComplex(Complex z1, Complex z2)
//复数乘法
Complex MulComplex(Complex z1, Complex z2)
//复数除法
Complex DivComplex(Complex z1, Complex z2)
//复数的辐角
RealNum ArgComplex(Complex z)之后继续更新关于顺序表的相关方法。
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