NAME¶

std::log10(std::complex) - std::log10(std::complex)

Synopsis¶

Defined in header <complex>
template< class T >
complex<T> log10( const 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 <iostream>
#include <cmath>
#include <complex>

int main()
{
std::complex<double> z(0, 1); // // r = 0, θ = pi/2
std::cout << "2*log10" << z << " = " << 2.*std::log10(z) << '\n';

std::complex<double> z2(sqrt(2)/2, sqrt(2)/2); // r = 1, θ = pi/4
std::cout << "4*log10" << z2 << " = " << 4.*std::log10(z2) << '\n';

std::complex<double> z3(-100, 0); // r = 100, θ = pi
std::cout << "log10" << z3 << " = " << std::log10(z3) << '\n';
std::complex<double> z4(-100, -0.0); // the other side of the cut
std::cout << "log10" << z4 << " (the other side of the cut) = "
<< std::log10(z4) << '\n'
<< "(note: pi/log(10) = " << acos(-1)/log(10) << ")\n";
}

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) (the other side of the cut) = (2,-1.36438)
(note: pi/log(10) = 1.36438)

See also¶

complex natural logarithm with the branch cuts along the
log(std::complex) negative real axis
(function template)
log10
log10f computes common (base 10) logarithm (\({\small \log_{10}{x}
log10l }\)log[10](x))
(C++11) (function)
(C++11)
log10(std::valarray) applies the function std::log10 to each element of valarray
(function template)