I

C

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Type support

Program utilities

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Error handling

Dynamic memory management

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Numerics

Input/output support

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Atomic operations (C11)

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Technical Specifications

Numerics

Common mathematical functions

Floating-point environment

Complex number arithmetics

Random number generation

Type-generic math

Complex number arithmetic

Types and the imaginary constant
complex _Complex_I CMPLX	imaginary _Imaginary_I I
Manipulation
cimag creal carg	cabs conj cproj
Power and exponential functions
cexp clog	cpow csqrt
Trigonometric functions
ccos csin ctan	cacos casin catan
Hyperbolic functions
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

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)

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)