The C programming language, as of C99, supports complex number math with the three built-in typesdouble _Complex,float _Complex, andlongdouble _Complex (see_Complex). When the header<complex.h> is included, the three complex number types are also accessible asdoublecomplex,floatcomplex,longdoublecomplex.

In addition to the complex types, the three imaginary types may be supported:double _Imaginary,float _Imaginary, andlongdouble _Imaginary (see_Imaginary). When the header<complex.h> is included, the three imaginary types are also accessible asdoubleimaginary,floatimaginary, andlongdoubleimaginary.

Standard arithmetic operators+,-,*,/ can be used with real, complex, and imaginary types in any combination.

[edit]Notes

The following function names arepotentially(since C23) reserved for future addition to<complex.h> and are not available for use in the programs that include that header:cerf,cerfc,cexp2,cexpm1,clog10,clog1p,clog2,clgamma,ctgamma,csinpi,ccospi,ctanpi,casinpi,cacospi,catanpi,ccompoundn,cpown,cpowr,crootn,crsqrt,cexp10m1,cexp10,cexp2m1,clog10p1,clog2p1,clogp1(since C23), along with their -f and -l suffixed variants.

Although the C standard names the inverse hyperbolic with "complex arc hyperbolic sine" etc., the inverse functions of the hyperbolic functions are the area functions. Their argument is the area of a hyperbolic sector, not an arc. The correct names are "complex inverse hyperbolic sine" etc. Some authors use "complex area hyperbolic sine" etc.

A complex or imaginary number is infinite if one of its parts is infinite, even if the other part is NaN.

A complex or imaginary number is finite if both parts are neither infinities nor NaNs.

A complex or imaginary number is a zero if both parts are positive or negative zeroes.

While MSVC does provide a<complex.h> header, it does not implement complex numbers as native types, but asstructs, which are incompatible with standard C complex types and do not support the+,-,*,/ operators.

[edit]Example

#include <complex.h>#include <stdio.h>#include <tgmath.h> int main(void){doublecomplex z1= I* I;// imaginary unit squaredprintf("I * I = %.1f%+.1fi\n",creal(z1),cimag(z1)); doublecomplex z2=pow(I,2);// imaginary unit squaredprintf("pow(I, 2) = %.1f%+.1fi\n",creal(z2),cimag(z2)); double PI=acos(-1);doublecomplex z3=exp(I* PI);// Euler's formulaprintf("exp(I*PI) = %.1f%+.1fi\n",creal(z3),cimag(z3)); doublecomplex z4=1+2* I, z5=1-2* I;// conjugatesprintf("(1+2i)*(1-2i) = %.1f%+.1fi\n",creal(z4* z5),cimag(z4* z5));}

I * I = -1.0+0.0ipow(I, 2) = -1.0+0.0iexp(I*PI) = -1.0+0.0i(1+2i)*(1-2i) = 5.0+0.0i

[edit]References

[edit]See also

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