[cmplx.over]

# 29 Numerics library [[numerics]](./#numerics)

## 29.4 Complex numbers [[complex.numbers]](complex.numbers#cmplx.over)

### 29.4.10 Additional overloads [cmplx.over]

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1173)

The following function templates have additional constexpr overloads:arg norm
conj proj
imag real

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1186)

The additional constexpr overloads are sufficient to ensure:

- [(2.1)](#2.1)

  If the argument has a floating-point type T,
then it is effectively cast to complex<T>[.](#2.1.sentence-1)

- [(2.2)](#2.2)

  Otherwise, if the argument has integer type,
then it is effectively cast to complex<double>[.](#2.2.sentence-1)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1198)

Function template pow has additional constexpr overloads sufficient to ensure,
for a call with one argument of type complex<T1> and
the other argument of type T2 or complex<T2>,
both arguments are effectively cast to complex<common_type_t<T1, T3>>,
where T3 isdouble if T2 is an integer type and T2 otherwise[.](#3.sentence-1)

If common_type_t<T1, T3> is not well-formed,
then the program is ill-formed[.](#3.sentence-2)