Specializations ofstd::complex for cv-unqualifiedstandard(until C++23)floating-point types areTriviallyCopyable(since C++23)LiteralTypes for representing and manipulatingcomplex number.

[edit]Template parameters

[edit]Member types

[edit]Member functions

[edit]Non-member functions

[edit]Helper types

[edit]Array-oriented access

For any objectz of typestd::complex<T>,reinterpret_cast<T(&)[2]>(z)[0] is the real part ofz andreinterpret_cast<T(&)[2]>(z)[1] is the imaginary part ofz.

For any pointer to an element of an array ofstd::complex<T> namedp and any valid array indexi,reinterpret_cast<T*>(p)[2* i] is the real part of the complex numberp[i], andreinterpret_cast<T*>(p)[2* i+1] is the imaginary part of the complex numberp[i].

The intent of this requirement is to preserve binary compatibility between the C++ library complex number types and theC language complex number types (and arrays thereof), which have an identical object representation requirement.

[edit]Implementation notes

In order to satisfy the requirements of array-oriented access, an implementation is constrained to store the real and imaginary parts of astd::complex specialization in separate and adjacent memory locations. Possible declarations for its non-static data members include:

• an array of typevalue_type[2], with the first element holding the real part and the second element holding the imaginary part (e.g. Microsoft Visual Studio);
• a single member of typevalue_type _Complex (encapsulating the correspondingC language complex number type) (e.g. GNU libstdc++);
• two members of typevalue_type, with the same member access, holding the real and the imaginary parts respectively (e.g. LLVM libc++).

An implementation cannot declare additional non-static data members that would occupy storage disjoint from the real and imaginary parts, and must ensure that the class template specialization does not contain anypadding bit. The implementation must also ensure that optimizations to array access account for the possibility that a pointer tovalue_type may be aliasing astd::complex specialization or array thereof.

[edit]Literals

[edit]Notes

[edit]Example

#include <cmath>#include <complex>#include <iomanip>#include <iostream>#include <ranges> int main(){usingnamespace std::complex_literals;std::cout<<std::fixed<<std::setprecision(1);     std::complex<double> z1= 1i* 1i;// imaginary unit squaredstd::cout<<"i * i = "<< z1<<'\n';     std::complex<double> z2=std::pow(1i,2);// imaginary unit squaredstd::cout<<"pow(i, 2) = "<< z2<<'\n'; constdouble PI=std::acos(-1);// or std::numbers::pi in C++20    std::complex<double> z3=std::exp(1i* PI);// Euler's formulastd::cout<<"exp(i * pi) = "<< z3<<'\n';     std::complex<double> z4=1.0+ 2i, z5=1.0- 2i;// conjugatesstd::cout<<"(1 + 2i) * (1 - 2i) = "<< z4* z5<<'\n'; constauto zz={0.0+ 1i,2.0+ 3i,4.0+ 5i};#if __cpp_lib_tuple_like >= 202311Lfor(double re: zz| std::views::keys)std::cout<< re<<' ';std::cout<<'\n';for(double im: zz| std::views::values)std::cout<< im<<' ';std::cout<<'\n';#elsefor(double re: zz| std::views::transform([](auto z){return z.real();}))std::cout<< re<<' ';std::cout<<'\n';for(double im: zz| std::views::transform([](auto z){return z.imag();}))std::cout<< im<<' ';std::cout<<'\n';#endif}

i * i = (-1.0,0.0)pow(i, 2) = (-1.0,0.0)exp(i * pi) = (-1.0,0.0)(1 + 2i) * (1 - 2i) = (5.0,0.0)0.0 2.0 4.01.0 3.0 5.0

[edit]Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

[edit]See also

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