std::log10(std::complex)

 

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std::complex

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complex::complex complex::operator= complex::real complex::imag	complex::operator+=complex::operator-=complex::operator*=complex::operator/=
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operator+operator- operator+operator-operator*operator/ operator==operator!= (until C++20)   operator<<operator>> get(std::complex) (C++26)	real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
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log   log10   exp
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tuple_size<std::complex> (C++26)
tuple_element<std::complex> (C++26)

 

Defined in header <complex>
template< class T > std::complex<T> log10( const std::complex<T>& z );

Computes complex common (base 10) logarithm of a complex value z with a branch cut along the negative real axis.

The behavior of this function is equivalent to std::log(z) / std::log(T(10)).

Parameters

z

-

complex value

Return value

Complex common logarithm of z.

Example

Run this code

#include <cmath>
#include <complex>
#include <iostream>
 
int main()
{
    std::complex<double> z(0.0, 1.0); // r = 0, θ = pi / 2
    std::cout << "2 * log10" << z << " = " << 2.0 * std::log10(z) << '\n';
 
    std::complex<double> z2(sqrt(2.0) / 2, sqrt(2.0) / 2); // r = 1, θ = pi / 4
    std::cout << "4 * log10" << z2 << " = " << 4.0 * std::log10(z2) << '\n';
 
    std::complex<double> z3(-100.0, 0.0); // r = 100, θ = pi
    std::cout << "log10" << z3 << " = " << std::log10(z3) << '\n';
    std::complex<double> z4(-100.0, -0.0); // the other side of the cut
    std::cout << "log10" << z4 << " = " << std::log10(z4) << " "
                 "(the other side of the cut)\n"
                 "(note: pi / log(10) = " << std::acos(-1.0) / std::log(10.0) << ")\n";
}

Possible output:

2 * log10(0,1) = (0,1.36438)
4 * log10(0.707107,0.707107) = (0,1.36438)
log10(-100,0) = (2,1.36438)
log10(-100,-0) = (2,-1.36438) (the other side of the cut)
(note: pi / log(10) = 1.36438)

See also

log(std::complex)	complex natural logarithm with the branch cuts along the negative real axis (function template)
log10log10flog10l (C++11)(C++11)	computes common (base 10) logarithm (\({\small\log_{10}{x}}\)log10(x)) (function)
log10(std::valarray)	applies the function std::log10 to each element of valarray (function template)