[complex.numbers.general]

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

## 29.4 Complex numbers [[complex.numbers]](complex.numbers#general)

### 29.4.1 General [complex.numbers.general]

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L180)

The header [<complex>](complex.syn#header:%3ccomplex%3e "29.4.2 Header <complex> synopsis [complex.syn]") defines a class template,
and numerous functions for representing and manipulating complex numbers[.](#1.sentence-1)

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L184)

The effect of instantiating the primary template of complex for any type
that is not a cv-unqualified floating-point type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))
is unspecified[.](#2.sentence-1)

Specializations of complex for cv-unqualified floating-point types
are trivially copyable literal types ([[basic.types.general]](basic.types.general#term.literal.type "6.9.1 General"))[.](#2.sentence-2)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L191)

If the result of a function is not mathematically defined or not in
the range of representable values for its type, the behavior is
undefined[.](#3.sentence-1)

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L196)

If z is an lvalue of type cv complex<T> then:

- [(4.1)](#4.1)

the expression reinterpret_cast<cv T(&)[2]>(z) is well-formed,

- [(4.2)](#4.2)

reinterpret_cast<cv T(&)[2]>(z)[0] designates the real part of z, and

- [(4.3)](#4.3)

reinterpret_cast<cv T(&)[2]>(z)[1] designates the imaginary part of z[.](#4.sentence-1)

Moreover, if a is an expression of type cv complex<T>* and the expression a[i] is well-defined for an integer expression i, then:

- [(4.4)](#4.4)

reinterpret_cast<cv T*>(a)[2 * i] designates the real part of a[i], and

- [(4.5)](#4.5)

reinterpret_cast<cv T*>(a)[2 * i + 1] designates the imaginary part of a[i][.](#4.sentence-2)