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(libc.info)Complex Numbers

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Complex Numbers
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   ISO C99 introduces support for complex numbers in C.  This is done
with a new type qualifier, `complex'.  It is a keyword if and only if
`complex.h' has been included.  There are three complex types,
corresponding to the three real types:  `float complex', `double
complex', and `long double complex'.

   To construct complex numbers you need a way to indicate the imaginary
part of a number.  There is no standard notation for an imaginary
floating point constant.  Instead, `complex.h' defines two macros that
can be used to create complex numbers.

 - Macro: const float complex _Complex_I
     This macro is a representation of the complex number "0+1i".
     Multiplying a real floating-point value by `_Complex_I' gives a
     complex number whose value is purely imaginary.  You can use this
     to construct complex constants:

          3.0 + 4.0i = `3.0 + 4.0 * _Complex_I'

     Note that `_Complex_I * _Complex_I' has the value `-1', but the
     type of that value is `complex'.

`_Complex_I' is a bit of a mouthful.  `complex.h' also defines a
shorter name for the same constant.

 - Macro: const float complex I
     This macro has exactly the same value as `_Complex_I'.  Most of the
     time it is preferable.  However, it causes problems if you want to
     use the identifier `I' for something else.  You can safely write

          #include <complex.h>
          #undef I

     if you need `I' for your own purposes.  (In that case we recommend
     you also define some other short name for `_Complex_I', such as
     `J'.)