< c‎ | numeric‎ | complex
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.


[edit] 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++)

[edit] Example

#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));


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

[edit] References

  • C11 standard (ISO/IEC 9899:2011):
  • 7.3.1/6 I (p: 188)
  • G.6/1 I (p: 537)
  • C99 standard (ISO/IEC 9899:1999):
  • 7.3.1/4 I (p: 170)
  • G.6/1 I (p: 472)

[edit] See also

the imaginary unit constant i
(macro constant) [edit]
the complex unit constant i
(macro constant) [edit]
constructs a complex number from real and imaginary parts
(function macro) [edit]
C++ documentation for operator""i