[complex.transcendentals]

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

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

### 29.4.8 Transcendentals [complex.transcendentals]

[🔗](#lib:acos,complex)

`template<class T> constexpr complex<T> acos(const complex<T>& x);
`

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L878)

*Returns*: The complex arc cosine of x[.](#1.sentence-1)

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L882)

*Remarks*: Behaves the same as the C function cacos[.](#2.sentence-1)

See also: ISO/IEC 9899:2024, 7.3.5.1

[🔗](#lib:asin,complex)

`template<class T> constexpr complex<T> asin(const complex<T>& x);
`

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L895)

*Returns*: The complex arc sine of x[.](#3.sentence-1)

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L899)

*Remarks*: Behaves the same as the C function casin[.](#4.sentence-1)

See also: ISO/IEC 9899:2024, 7.3.5.2

[🔗](#lib:atan,complex)

`template<class T> constexpr complex<T> atan(const complex<T>& x);
`

[5](#5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L912)

*Returns*: The complex arc tangent of x[.](#5.sentence-1)

[6](#6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L916)

*Remarks*: Behaves the same as the C function catan[.](#6.sentence-1)

See also: ISO/IEC 9899:2024, 7.3.5.3

[🔗](#lib:acosh,complex)

`template<class T> constexpr complex<T> acosh(const complex<T>& x);
`

[7](#7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L929)

*Returns*: The complex arc hyperbolic cosine of x[.](#7.sentence-1)

[8](#8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L933)

*Remarks*: Behaves the same as the C function cacosh[.](#8.sentence-1)

See also: ISO/IEC 9899:2024, 7.3.6.1

[🔗](#lib:asinh,complex)

`template<class T> constexpr complex<T> asinh(const complex<T>& x);
`

[9](#9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L946)

*Returns*: The complex arc hyperbolic sine of x[.](#9.sentence-1)

[10](#10)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L950)

*Remarks*: Behaves the same as the C function casinh[.](#10.sentence-1)

See also: ISO/IEC 9899:2024, 7.3.6.2

[🔗](#lib:atanh,complex)

`template<class T> constexpr complex<T> atanh(const complex<T>& x);
`

[11](#11)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L963)

*Returns*: The complex arc hyperbolic tangent of x[.](#11.sentence-1)

[12](#12)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L967)

*Remarks*: Behaves the same as the C function catanh[.](#12.sentence-1)

See also: ISO/IEC 9899:2024, 7.3.6.3

[🔗](#lib:cos,complex)

`template<class T> constexpr complex<T> cos(const complex<T>& x);
`

[13](#13)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L979)

*Returns*: The complex cosine of x[.](#13.sentence-1)

[🔗](#lib:cosh,complex)

`template<class T> constexpr complex<T> cosh(const complex<T>& x);
`

[14](#14)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L990)

*Returns*: The complex hyperbolic cosine of x[.](#14.sentence-1)

[🔗](#lib:exp,complex)

`template<class T> constexpr complex<T> exp(const complex<T>& x);
`

[15](#15)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1001)

*Returns*: The complex base-e exponential of x[.](#15.sentence-1)

[🔗](#lib:log,complex)

`template<class T> constexpr complex<T> log(const complex<T>& x);
`

[16](#16)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1012)

*Returns*: The complex natural (base-e) logarithm of x[.](#16.sentence-1)

For all x,imag(log(x)) lies in the interval [−π, π][.](#16.sentence-2)

[*Note [1](#note-1)*:

The semantics of this function are intended to be the same in C++
as they are for clog in C[.](#16.sentence-3)

— *end note*]

[17](#17)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1021)

*Remarks*: The branch cuts are along the negative real axis[.](#17.sentence-1)

[🔗](#lib:log10,complex)

`template<class T> constexpr complex<T> log10(const complex<T>& x);
`

[18](#18)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1032)

*Returns*: The complex common (base-10) logarithm of x, defined aslog(x) / log(10)[.](#18.sentence-1)

[19](#19)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1037)

*Remarks*: The branch cuts are along the negative real axis[.](#19.sentence-1)

[🔗](#lib:pow,complex)

`template<class T> constexpr complex<T> pow(const complex<T>& x, const complex<T>& y);
template<class T> constexpr complex<T> pow(const complex<T>& x, const T& y);
template<class T> constexpr complex<T> pow(const T& x, const complex<T>& y);
`

[20](#20)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1050)

*Returns*: The complex power of base x raised to the yth power,
defined asexp(y * log(x))[.](#20.sentence-1)

The value returned forpow(0, 0) is implementation-defined[.](#20.sentence-2)

[21](#21)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1059)

*Remarks*: The branch cuts are along the negative real axis[.](#21.sentence-1)

[🔗](#lib:sin,complex)

`template<class T> constexpr complex<T> sin(const complex<T>& x);
`

[22](#22)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1070)

*Returns*: The complex sine of x[.](#22.sentence-1)

[🔗](#lib:sinh,complex)

`template<class T> constexpr complex<T> sinh(const complex<T>& x);
`

[23](#23)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1081)

*Returns*: The complex hyperbolic sine of x[.](#23.sentence-1)

[🔗](#lib:sqrt,complex)

`template<class T> constexpr complex<T> sqrt(const complex<T>& x);
`

[24](#24)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1092)

*Returns*: The complex square root of x, in the range of the right
half-plane[.](#24.sentence-1)

[*Note [2](#note-2)*:

The semantics of this function are intended to be the same in C++
as they are for csqrt in C[.](#24.sentence-2)

— *end note*]

[25](#25)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1101)

*Remarks*: The branch cuts are along the negative real axis[.](#25.sentence-1)

[🔗](#lib:tan,complex)

`template<class T> constexpr complex<T> tan(const complex<T>& x);
`

[26](#26)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1112)

*Returns*: The complex tangent of x[.](#26.sentence-1)

[🔗](#lib:tanh,complex)

`template<class T> constexpr complex<T> tanh(const complex<T>& x);
`

[27](#27)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L1123)

*Returns*: The complex hyperbolic tangent of x[.](#27.sentence-1)