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Showing content from https://en.cppreference.com/w/cpp/language/../algorithm/../ranges/../numeric/complex/log10.html below:

std::log10(std::complex) - cppreference.com

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)).

Complex common logarithm of z.

#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)

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