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## 20.10 Projections, Conjugates, and Decomposing of Complex Numbers

ISO C99 also defines functions that perform basic operations on complex numbers, such as decomposition and conjugation. The prototypes for all these functions are in `complex.h'. All functions are available in three variants, one for each of the three complex types.

Function: double creal (complex double z)
Function: float crealf (complex float z)
Function: long double creall (complex long double z)
These functions return the real part of the complex number z.

Function: double cimag (complex double z)
Function: float cimagf (complex float z)
Function: long double cimagl (complex long double z)
These functions return the imaginary part of the complex number z.

Function: complex double conj (complex double z)
Function: complex float conjf (complex float z)
Function: complex long double conjl (complex long double z)
These functions return the conjugate value of the complex number z. The conjugate of a complex number has the same real part and a negated imaginary part. In other words, `conj(a + bi) = a + -bi'.

Function: double carg (complex double z)
Function: float cargf (complex float z)
Function: long double cargl (complex long double z)
These functions return the argument of the complex number z. The argument of a complex number is the angle in the complex plane between the positive real axis and a line passing through zero and the number. This angle is measured in the usual fashion and ranges from 0 to 2&#38;pi;.

`carg` has a branch cut along the positive real axis.

Function: complex double cproj (complex double z)
Function: complex float cprojf (complex float z)
Function: complex long double cprojl (complex long double z)
These functions return the projection of the complex value z onto the Riemann sphere. Values with a infinite imaginary part are projected to positive infinity on the real axis, even if the real part is NaN. If the real part is infinite, the result is equivalent to

 ```INFINITY + I * copysign (0.0, cimag (z)) ```

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