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# I

From cppreference.com
< 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

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

### [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

_Imaginary_I (C99) | the imaginary unit constant i (macro constant) [edit]
_Complex_I (C99) | the complex unit constant i (macro constant) [edit]
CMPLX CMPLXF CMPLXL (C11)(C11)(C11) | constructs a complex number from real and imaginary parts (function macro) [edit]
C++ documentation for operator""i

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