I
| Types and the imaginary constant | |||||||||||||||||||||||||||||||
|
| ||||||||||||||||||||||||||||||
| Manipulation | |||||||||||||||||||||||||||||||
| Power and exponential functions | |||||||||||||||||||||||||||||||
| Trigonometric functions | |||||||||||||||||||||||||||||||
| Hyperbolic functions | |||||||||||||||||||||||||||||||
| 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.
Contents |
[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)); }
Output:
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
| (C99) |
the imaginary unit constant i (macro constant) [edit] |
| (C99) |
the complex unit constant i (macro constant) [edit] |
| (C11)(C11)(C11) |
constructs a complex number from real and imaginary parts (function macro) [edit] |
| C++ documentation for operator""i
| |
