29 Numerics library [numerics]

29.4 Complex numbers [complex.numbers]

29.4.6 Non-member operations [complex.ops]

template<class T> constexpr complex<T> operator+(const complex<T>& lhs);

Returns: complex<T>(lhs).

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template<class T> constexpr complex<T> operator+(const complex<T>& lhs, const complex<T>& rhs);
template<class T> constexpr complex<T> operator+(const complex<T>& lhs, const T& rhs);
template<class T> constexpr complex<T> operator+(const T& lhs, const complex<T>& rhs);

Returns: complex<T>(lhs) += rhs.

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template<class T> constexpr complex<T> operator-(const complex<T>& lhs);

Returns: complex<T>(-lhs.real(),-lhs.imag()).

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template<class T> constexpr complex<T> operator-(const complex<T>& lhs, const complex<T>& rhs);
template<class T> constexpr complex<T> operator-(const complex<T>& lhs, const T& rhs);
template<class T> constexpr complex<T> operator-(const T& lhs, const complex<T>& rhs);

Returns: complex<T>(lhs) -= rhs.

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template<class T> constexpr complex<T> operator*(const complex<T>& lhs, const complex<T>& rhs);
template<class T> constexpr complex<T> operator*(const complex<T>& lhs, const T& rhs);
template<class T> constexpr complex<T> operator*(const T& lhs, const complex<T>& rhs);

Returns: complex<T>(lhs) *= rhs.

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template<class T> constexpr complex<T> operator/(const complex<T>& lhs, const complex<T>& rhs);
template<class T> constexpr complex<T> operator/(const complex<T>& lhs, const T& rhs);
template<class T> constexpr complex<T> operator/(const T& lhs, const complex<T>& rhs);

Returns: complex<T>(lhs) /= rhs.

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template<class T> constexpr bool operator==(const complex<T>& lhs, const complex<T>& rhs);
template<class T> constexpr bool operator==(const complex<T>& lhs, const T& rhs);

Returns: lhs.real() == rhs.real() && lhs.imag() == rhs.imag().

Remarks: The imaginary part is assumed to be T(), or 0.0, for the T arguments.

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template<class T, class charT, class traits>
  basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, complex<T>& x);

Preconditions: The input values are convertible to T.

Effects: Extracts a complex number x of the form: u, (u), or (u,v), where u is the real part and v is the imaginary part ([istream.formatted]).

If bad input is encountered, calls is.setstate(ios_base::failbit) (which may throw ios_base::failure ([iostate.flags])).

Returns: is.

Remarks: This extraction is performed as a series of simpler extractions.

Therefore, the skipping of whitespace is specified to be the same for each of the simpler extractions.

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template<class T, class charT, class traits>
  basic_ostream<charT, traits>& operator<<(basic_ostream<charT, traits>& o, const complex<T>& x);

Effects: Inserts the complex number x onto the stream o as if it were implemented as follows: basic_ostringstream<charT, traits> s; s.flags(o.flags()); s.imbue(o.getloc()); s.precision(o.precision()); s << '(' << x.real() << ',' << x.imag() << ')'; return o << s.str();

[Note 1:

In a locale in which comma is used as a decimal point character, the use of comma as a field separator can be ambiguous.

Inserting showpoint into the output stream forces all outputs to show an explicit decimal point character; as a result, all inserted sequences of complex numbers can be extracted unambiguously.

— end note]