How to work with complex numbers in C

Question

How can I work with complex numbers in C  I see there is a complex h header file  but it doesn t give me much information about how to use it  How to access real and imaginary parts in an efficient way  Is there native functions to get module and phase

User · Answer

The notion of complex numbers was introduced in mathematics, from the need of calculating negative quadratic roots. Complex number concept was taken by a variety of engineering fields.

Today that complex numbers are widely used in advanced engineering domains such as physics, electronics, mechanics, astronomy, etc...

Real and imaginary part, of a negative square root example:

#include <stdio.h>   
#include <complex.h>

int main() 
{
    int negNum;

    printf("Calculate negative square roots:\n"
           "Enter negative number:");

    scanf("%d", &negNum);

    double complex negSqrt = csqrt(negNum);

    double pReal = creal(negSqrt);
    double pImag = cimag(negSqrt);

    printf("\nReal part %f, imaginary part %f"
           ", for negative square root.(%d)",
           pReal, pImag, negNum);

    return 0;
}

User · Answer

Complex types are in the C language since C99 standard  -std c99 option of GCC   Some compilers may implement complex types even in more earlier modes  but this is non-standard and non-portable extension  e g  IBM XL  GCC  may be intel         You can start from http   en wikipedia org wiki Complex h - it gives a description of functions from complex h  This manual http   pubs opengroup org onlinepubs 009604499 basedefs complex h html also gives some info about macros   To declare a complex variable  use     double  Complex  a            use c  functions without suffix   or     float  Complex   b            use c f functions - with f suffix   long double  Complex c        use c l functions - with l suffix   To give a value into complex  use  Complex I macro from complex h     float  Complex d   2 0f   2 0f  Complex I     actually there can be some problems here with  0 -0i  numbers and NaNs in single half of complex   Module is cabs a  cabsl c  cabsf b   Real part is creal a   Imaginary is cimag a   carg a  is for complex argument   To directly access  read write  real an imag part you may use this unportable GCC-extension      real   a   1 4     imag   a   2 0   float b     real   a

User · Answer

For convenience  one may include tgmath h library for the type generate macros  It creates the same function name as the double version for all type of variable  For example  For example  it defines a sqrt   macro that expands to the sqrtf     sqrt     or sqrtl   function  depending on the type of argument provided    So one don t need to remember the corresponding function name for different type of variables    include  lt stdio h gt   include  lt tgmath h gt   for the type generate macros    include  lt complex h gt   for easier declare complex variables and complex unit I  int main void        double complex z1 1  4  M PI 1  4  M PI I   M PI is just pi 3 1415        double complex z2  z3  z4  z5        z2 exp z1       z3 sin z1       z4 sqrt z1       z5 log z1        printf  exp z1   lf    lf I n   creal z2  cimag z2        printf  sin z1   lf    lf I n   creal z3  cimag z3        printf  sqrt z1   lf    lf I n   creal z4  cimag z4        printf  log z1   lf    lf I n   creal z5  cimag z5         return 0

User · Answer

To extract the real part of a complex-valued expression z  use the notation as   real   z  Similarly  use   imag   attribute on the z to extract the imaginary part    For example     complex   float z  float r  float i  r     real   z  i     imag   z    r is the real part of the complex number  z  i is the imaginary part of the complex number  z

User · Answer

This code will help you  and it s fairly self-explanatory    include  lt stdio h gt          Standard Library of Input and Output     include  lt complex h gt        Standard Library of Complex Numbers     int main          double complex z1   1 0   3 0   I      double complex z2   1 0 - 4 0   I       printf  Working with complex numbers  n v         printf  Starting values  Z1     2f     2fi tZ2     2f    2fi n   creal z1   cimag z1   creal z2   cimag z2         double complex sum   z1   z2      printf  The sum  Z1   Z2     2f    2fi n   creal sum   cimag sum         double complex difference   z1 - z2      printf  The difference  Z1 - Z2     2f    2fi n   creal difference   cimag difference         double complex product   z1   z2      printf  The product  Z1 x Z2     2f    2fi n   creal product   cimag product         double complex quotient   z1   z2      printf  The quotient  Z1   Z2     2f    2fi n   creal quotient   cimag quotient         double complex conjugate   conj z1       printf  The conjugate of Z1     2f    2fi n   creal conjugate   cimag conjugate         return 0       nbsp  with   creal z1   get the real part  for float crealf z1   for long double creall z1    cimag z1   get the imaginary part  for float cimagf z1   for long double cimagl z1    Another important point to remember when working with complex numbers is that functions like cos    exp   and sqrt   must be replaced with their complex forms  e g  ccos    cexp    csqrt

[c] How to work with complex numbers in C?

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