C++
| Language | ||||
| Standard library headers | ||||
| Concepts | ||||
| Utilities library | ||||
| Strings library | ||||
| Containers library | ||||
| Algorithms library | ||||
| Iterators library | ||||
| Numerics library | ||||
| Input/output library | ||||
| Localizations library | ||||
| Regular expressions library (C++11) | ||||
| Atomic operations library (C++11) | ||||
| Thread support library (C++11) | ||||
| Filesystem library (C++17) | ||||
| Technical Specifications |
Numerics library
| Common mathematical functions | ||||
| Special mathematical functions | ||||
| Floating-point environment (C++11) | ||||
| Complex numbers | ||||
| Numeric arrays | ||||
| Pseudo-random number generation | ||||
| Compile-time rational arithmetic (C++11) | ||||
| Numeric algorithms | ||||
gcd (C++17) | ||||
lcm (C++17) | ||||
| Generic numeric operations | ||||
iota (C++11) | ||||
accumulate | ||||
inner_product | ||||
adjacent_difference | ||||
partial_sum |
std::complex
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complex::complex | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
complex::operator= | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
complex::real | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
complex::imag | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
complex::operator+=complex::operator-=complex::operator*=complex::operator/= | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Non-member functions | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| Exponential functions | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
exp | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
log | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
log10 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Power functions | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
pow | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
sqrt | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Trigonometric functions | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| Hyperbolic functions | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| Defined in header | ||
| template< class T > | (1) | |
| template<> class complex<float>; | (2) | |
| template<> class complex<double>; | (3) | |
| template<> class complex<long double>; | (4) | |
The specializations std::complex<float>, std::complex<double>, and std::complex<long double> are LiteralTypes for representing and manipulating complex numbers.
The effect of instantiating the template complex for any other type is unspecified.
Member types
| Member type | Definition |
value_type | T |
Member functions
| (constructor) | constructs a complex number (public member function) |
| operator= | assigns the contents (public member function) |
| real | accesses the real part of the complex number (public member function) |
| imag | accesses the imaginary part of the complex number (public member function) |
| operator+=operator-=operator/=operator*= | compound assignment of two complex numbers or a complex and a scalar (public member function) |
Non-member functions
| operator+operator- | applies unary operators to complex numbers (function template) |
| operator+operator-operator*operator/ | performs complex number arithmetics on two complex values or a complex and a scalar (function template) |
| operator==operator!= | compares two complex numbers or a complex and a scalar (function template) |
| operator<<operator>> | serializes and deserializes a complex number (function template) |
| real | returns the real component (function template) |
| imag | returns the imaginary component (function template) |
| abs(std::complex) | returns the magnitude of a complex number (function template) |
| arg | returns the phase angle (function template) |
| norm | returns the squared magnitude (function template) |
| conj | returns the complex conjugate (function template) |
| proj (C++11) | returns the projection onto the Riemann sphere (function template) |
| polar | constructs a complex number from magnitude and phase angle (function template) |
Exponential functions | |
| exp(std::complex) | complex base e exponential (function template) |
| log(std::complex) | complex natural logarithm with the branch cuts along the negative real axis (function template) |
| log10(std::complex) | complex common logarithm with the branch cuts along the negative real axis (function template) |
Power functions | |
| pow(std::complex) | complex power, one or both arguments may be a complex number (function template) |
| sqrt(std::complex) | complex square root in the range of the right half-plane (function template) |
Trigonometric functions | |
| sin(std::complex) | computes sine of a complex number (sin(z)) (function template) |
| cos(std::complex) | computes cosine of a complex number (cos(z)) (function template) |
| tan(std::complex) | computes tangent of a complex number (tan(z)) (function template) |
| asin(std::complex) (C++11) | computes arc sine of a complex number (arcsin(z)) (function template) |
| acos(std::complex) (C++11) | computes arc cosine of a complex number (arccos(z)) (function template) |
| atan(std::complex) (C++11) | computes arc tangent of a complex number (arctan(z)) (function template) |
Hyperbolic functions | |
| sinh(std::complex) | computes hyperbolic sine of a complex number (sh(z)) (function template) |
| cosh(std::complex) | computes hyperbolic cosine of a complex number (ch(z)) (function template) |
| tanh(std::complex) | computes hyperbolic tangent of a complex number (function template) |
| asinh(std::complex) (C++11) | computes area hyperbolic sine of a complex number (function template) |
| acosh(std::complex) (C++11) | computes area hyperbolic cosine of a complex number (function template) |
| atanh(std::complex) (C++11) | computes area hyperbolic tangent of a complex number (function template) |
Non-static data members
For any object For any pointer to an element of an array of These requirements essentially limit implementation of each of the three specializations of std::complex to declaring two and only two non-static data members, of type The intent of this requirement is to preserve binary compatibility between the C++ library complex number types and the C language complex number types (and arrays thereof), which have an identical object representation requirement. | (since C++11) |
Literals
| Defined in inline namespace | |
| operator""ifoperator""ioperator""il (C++14) | A std::complex literal representing pure imaginary number (function) |
Example
Run this code
#include <iostream>#include <iomanip>#include <complex>#include <cmath>int main(){ using namespace std::complex_literals; std::cout << std::fixed << std::setprecision(1); std::complex<double> z1 = 1i * 1i; // imaginary unit squared std::cout << "i * i = " << z1 << '\n'; std::complex<double> z2 = std::pow(1i, 2); // imaginary unit squared std::cout << "pow(i, 2) = " << z2 << '\n'; double PI = std::acos(-1); std::complex<double> z3 = std::exp(1i * PI); // Euler's formula std::cout << "exp(i * pi) = " << z3 << '\n'; std::complex<double> z4 = 1. + 2i, z5 = 1. - 2i; // conjugates std::cout << "(1+2i)*(1-2i) = " << z4*z5 << '\n';}
Output:
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)
See also
C documentation for Complex number arithmetic
