[C language] header file of complex number four operations and complex number operations

Catalog

One 、 Four operations of complex numbers

Two 、 Plural header file #include<complex.h>

3、 ... and 、 Some broken thoughts

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One 、 Four operations of complex numbers

(1) computing method

1. Add ：（a+bi）+(c+di)=(a+c)+(c+d)i【 The real part is added to the real part , Add the imaginary part and the imaginary step 】

2. Subtraction ：（a+bi）-(c+di)=(a-c)+(c-d)i【 The real part is subtracted from the real part , The imaginary part is subtracted from the imaginary step 】

3. Multiplication ：（a+bi）(c+di)=ac+adi+cdi+bdi*i=(ac-bd)+(bc+ad)i【 Ordinary polynomial multiplication ;i^2=-1】

4. division ：（a+bi）/(c+di)=（a+bi）(c-di)/((c+di)(c+di))=((ac+bd)+(bc-ad)i)/(c^2+d^2)【 The conjugate complex number of the numerator and denominator multiplied by the denominator , Then there is multiplication , Next is multiplication 】

(2) Example ： This question requires the preparation of procedures , Calculation 2 The sum of two plurals 、 Bad 、 product 、 merchant .

Input format ：

Type in a line and press a1 b1 a2 b2 The format of 2 Plural C1=a1+b1i and C2=a2+b2i The real part and the virtual part of . Title assurance C2 Not for 0.

Output format ：

Respectively in 4 In line with (a1+b1i) Operator (a2+b2i) = result Format order output 2 The sum of two plurals 、 Bad 、 product 、 merchant , The number is accurate to the decimal point 1 position . If the real or imaginary part of the result is 0, No output . If the result is 0, The output 0.0.

sample input 1：

 2 3.08 -2.04 5.06

sample output 1：

 (2.0+3.1i) + (-2.0+5.1i) = 8.1i
 (2.0+3.1i) - (-2.0+5.1i) = 4.0-2.0i
 (2.0+3.1i) * (-2.0+5.1i) = -19.7+3.8i
 (2.0+3.1i) / (-2.0+5.1i) = 0.4-0.6i

sample input 2：

 1 1 -1 -1.01

sample output 2：

 (1.0+1.0i) + (-1.0-1.0i) = 0.0
 (1.0+1.0i) - (-1.0-1.0i) = 2.0+2.0i
 (1.0+1.0i) * (-1.0-1.0i) = -2.0i
 (1.0+1.0i) / (-1.0-1.0i) = -1.0

 #include<stdio.h>
 float a, b, c, d; 
 ​
 void sign(char op);
 void operation(float e,float f,char op);  
 int main(void)
 {
     scanf("%f%f%f%f", &a, &b, &c, &d);
     operation(a+c, b+d, '+');
     operation(a-c, b-d, '-');
     operation(a*c - b*d, a*d + b*c, '*');
     operation((a*c + b*d) / (c*c + d*d), (b*c - a*d) / (c*c + d*d), '/');
     return 0;
 }
  
 void sign(char op)
 {
     printf("(%.1f", a);
     if(b>=0)
         printf("+"); 
     printf("%.1fi) %c (%.1f", b, op, c);
     if(d>=0)
         printf("+");        
     printf("%.1fi) = ", d);
 }
  
 void operation(float e,float f,char op)
 {
     sign(op);
     if((int)(e*10))
         printf("%.1f", e);
     if((int)(f*10))
     {
         if ((f > 0) && (int)(e*10))
             printf("+");
         printf("%.1fi", f);
     }
     else if (!(int)(e*10))
         printf("0.0");
     printf("\n");
 }

 

Two 、 Plural header file #include <complex.h>

（1）C There are three types in a language that can store plural numbers

float_Complex: Both the real part and the imaginary part are float type

double_Complex: Both the real part and the imaginary part are double type

long double_Complex: Both the real part and the imaginary part are long type

for example ：double_Complex x;

notes ：C99 Support for plural , No header files are required with this definition method .

（2） Add header file #include <complex.h>, You can use it complex Instead of _Complex, This header defines the imaginary part as 'I', So defining such a complex number can be like this float complex z=a+bI;

(3) macro

Macro name	value
complex	_Complex
_Complex_I	An imaginary unit , The type is const float_Complex
I	_Complex_I

there I Instead of Complex_I By analogy bool(#include <stdbool> Medium ) and Bool equally

The assignment method of complex numbers is as follows ：doubel complex dc=2.0+3.5*I;

 

(4) Several functions

1.double real_part=creal(z);// obtain Z The real part of

2.double imag_part=cimag(z)// obtain Z The imaginary part of

Processing float and long double Type , use crealf() and creall(),cimagf() and cimagl().【 understand ： With double complex Benchmarking 】

3. extension ： Allow multiplication and division of complex numbers with absolute values , But there must be CX_LIMITED_RANGE Compilation tips for

 

 

 

 

 

 

4. Complex function expansion

 

 

 

 

Classification of complex functions ： Trigonometric functions 、 Hyperbolic function 、 Exponential and logarithmic functions 、 Power function and operation function .

The operation function is like this

 

（2） Example ： find the root of the quadratic equation

Particular attention ： The solution of virtual root of quadratic equation in one variable ： Turn negative numbers into positive numbers , But we need to add one after him i

 

therefore , Real component =-b/（2a）, Imaginary part =sqrt(-dert)/(2a).

describe

Input from keyboard a, b, c Value , Program to calculate and output the univariate quadratic equation ax2 + bx + c = 0 The root of the , When a = 0 when , Output “Not quadratic equation”, When a ≠ 0 when , according to △ = b2 - 4ac Calculate and output the root of the equation in three cases .

Input description ：

Multi group input , a line , Contains three floating point numbers a, b, c, Separated by a space , Represents a quadratic equation of one variable ax2 + bx + c = 0 The coefficient of .

Output description ：

Enter... For each group , Output one line , Output univariate quadratic equation ax2 + bx +c = 0 The root of .

If a = 0, Output “Not quadratic equation”;

If a ≠ 0, There are three situations ：

△ = 0, Then two real roots are equal , The output form is ：x1=x2=....

△ > 0, Then the two real roots are unequal , The output form is ：x1=...;x2=..., among x1 <= x2.

△ < 0, There are two virtual roots , The output ：x1=* Real component - Imaginary part i;x2= Real component + Imaginary part i**, namely x1 The imaginary part coefficient of is less than or equal to x2 Imaginary part coefficient of , The real part is 0 You cannot omit . Real component = -b / (2a), Imaginary part = sqrt(-△ ) / (2*a)

All real parts shall be accurate to the decimal point 2 position , Numbers 、 There is no space between symbols .

Example 1

Input ：

 2.0 7.0 1.0

Output ：

 x1=-3.35;x2=-0.15

 #include <stdio.h>
 #include <math.h>
 double zhengen(double m, double n, double d);// Realize the formula function of finding the root of a quadratic equation of one variable +
 double fugen(double m, double n, double d);// Realize the formula function of finding the root of a quadratic equation of one variable -
 double shibu(double m, double n);
 double xubu(double m, double d);
 int main()
 {
     double a = 0, b = 0, c = 0,x1=0,x2=0;
     while(scanf("%lf %lf %lf", &a, &b, &c)!=EOF)
     {
         double derta = pow(b, 2) - 4 * a * c;
         if (a != 0)// The first parameter is not 0
         {
             if (derta == 0)//①=0
             {
                 if(b==0)// This can also be lost directly , Just a little more 
                     printf("x1=x2=0.00\n");
                 else
                 {
                     x1 = x2 = zhengen(a,b,derta);
                     printf("x1=x2=%.2lf\n", x1);
                 }
 ​
             }
             else if (derta > 0)//②>0
             {// Here is to assign the larger solution to the positive root , The smaller solution is assigned to the negative root 
                 x1 =( zhengen(a, b, derta)> fugen(a, b, derta)) ? fugen(a, b, derta) : zhengen(a, b, derta);
                 x2 =(zhengen(a, b, derta) > fugen(a, b, derta)) ? zhengen(a, b, derta) : fugen(a, b, derta);
                 printf("x1=%.2lf;x2=%.2lf\n",x1,x2);
             }
             else if (derta < 0)//③<0—— imaginary root 
             {
                 if(xubu(a,derta)<0)// Pay attention to the difference between plus and minus signs 
                     printf("x1=%.2lf%.2lfi;x2=%.2lf+%.2lfi\n",shibu(a, b),xubu(a, derta), shibu(a, b), -xubu(a, derta));
                 else
                     printf("x1=%.2lf-%.2lfi;x2=%.2lf+%.2lfi\n",shibu(a, b),xubu(a, derta), shibu(a, b), xubu(a, derta));
             }
         }
         else
         {
             printf("Not quadratic equation");// Not a quadratic equation 
         }
     }
     return 0;
 }
 double zhengen(double m, double n, double d)// Realize the formula function of finding the root of a quadratic equation of one variable +
 {
     double x = 0;
     x = (-n + sqrt(d)) / (2 * m);
     return x;
 }
 double fugen(double m, double n, double d)// Realize the formula function of finding the root of a quadratic equation of one variable -
 {
     double x = 0;
     x = (-n - sqrt(d)) / (2 * m);
     return x;
 }
 double shibu(double m, double n)
 {
     double s = 0;
     s = (-n) / (2 * m);
     return s;
 }
 double xubu(double m, double d)
 {
     double xu = 0;
     xu = sqrt(-d) / (2 * m);
     return xu;
 }

 

3、 ... and 、 Some broken thoughts

This summary is because I have accomplished the programming problem of quadratic equation of one variable , The virtual root is not particularly understood , Just look back , The original title said their method , I just didn't take it seriously . Then when I do the experiment in class today , I found that there are four operations of that complex number , I'm not very good at plural arithmetic myself , Add programming , double buff, My day , At that time, there was only one head , Two big , But I think of the problem of virtual root that I did before , Just think that I must break it this time . Can't be like before , Always find problems , Instead of solving the problem , Just wait for others to feed them , You may not eat this knowledge point . Finally, I watched myself slide a little , Others rise a little , My heart is not willing to , But there's nothing we can do , Run around .

This time I actively associate , It is a good start to actively summarize the content of the plural . come on. ~ Okay , That's the end of the bullshit , Let's review what we did this time

1. Arithmetic operation of complex numbers / arithmetic 【 Calculation rules and computer representation —— What we use here is 4 individual operation function , Parameters are two numbers and an operator , The two parameters are the real part and imaginary part calculated according to the operation rules of negative numbers ; Then a function that mainly prints the equation sign（ Here we need to pay special attention to the printing of symbols inside, such as the real part / Positive and negative of imaginary part ==>+/-）】

2. One variable quadratic equation 【 The whole is divided into 2 In this case a>0 And a<0, among a>0 It is divided into 3 In this case , One is dert>0,dert<0,dert=0. then dert<0 The real part needs to be calculated （-b/2a） Deficiency part of harmony (sqrt(-dert)/2a); There are many calculations here , It will be more convenient for us to encapsulate it into a function ——zhengen+fugen+shibu+xubu】

3. Header file #include <complex.h> With understanding , Like defining 3 Two types of variables , Get a real part with a complex number , Get the imaginary part of a complex number . As for the rest, it's just expanding reading , There are no instances and application scenarios , Understanding will not be in place . for instance I、complex Etc. are defined by macros , There are also some complex functions （ usually c At the beginning , such as csin） Some understanding .