std::log10(std::complex) (3) Linux Manual Page

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 negative real axis
log(std::complex) (function template)
log10
log10f
log10l computes common (base 10) logarithm (log10(x))
                     (function)
(C++11)
(C++11)
                     applies the function std::log10 to each element of valarray
log10(std::valarray) (function template)