I

 

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Complex number arithmetic

Types and the imaginary constant
complex _Complex_I CMPLX	imaginary _Imaginary_I I
Manipulation
cimag creal carg	cabs conj cproj
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cexp clog	cpow csqrt
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ccos csin ctan	cacos casin catan
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ccosh csinh ctanh	cacosh casinh catanh

 

Defined in header <complex.h>
#define I /* unspecified */		(since C99)

The I macro expands to either _Complex_I or _Imaginary_I. If the implementation does not support imaginary types, then the macro always expands to _Complex_I.

A program may undefine and perhaps then redefine the macro I.

Notes

The macro is not named i, which is the name of the imaginary unit in mathematics, because the name i was already used in many C programs, e.g. as a loop counter variable.

The macro I is often used to form complex numbers, with expressions such as x + y*I. If I is defined as _Complex_I, then such expression may create a value with imaginary component +0.0 even when y is -0.0, which is significant for complex number functions with branch cuts. The macro CMPLX provides a way to construct a complex number precisely.

GCC provides a non-portable extension that allows imaginary constants to be specified with the suffix i on integer literals: 1.0fi, 1.0i, and 1.0li are imaginary units in GNU C. A similar approach is part of standard C++ as of C++14 (1.0if, 1.0i, and 1.0il are the imaginary units in C++)

Example

Run this code

#include <stdio.h>
#include <complex.h>
 
int main(void)
{
    printf("I = %.1f%+.1fi\n", creal(I), cimag(I));
 
    double complex z1 = I * I;     // imaginary unit squared
    printf("I * I = %.1f%+.1fi\n", creal(z1), cimag(z1));
 
    double complex z = 1.0 + 2.0*I; // usual way to form a complex number pre-C11
    printf("z = %.1f%+.1fi\n", creal(z), cimag(z));
}

Output:

I = 0.0+1.0i
I * I = -1.0+0.0i
z = 1.0+2.0i

See also

_Imaginary_I (C99)	the imaginary unit constant i (macro constant)
_Complex_I (C99)	the complex unit constant i (macro constant)
CMPLXCMPLXFCMPLXL (C11)(C11)(C11)	constructs a complex number from real and imaginary parts (function macro)
C++ documentation for operator""i