std::log10(std::complex)(3)

Hey bestie 💖 this is the std::log10(std::complex)(3) page from the C++ Standard Libary manual — and no, we are not gatekeeping complex log math today.

💖 NAME 💖

std::log10(std::complex) — std::log10(std::complex). That's the whole NAME line, and honestly it's giving self-titled debut album 💅.

🌸 Synopsis 🌸

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

Okay so this template computes the 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)). That's the tea ☕✨.

🎀 Parameters 🎀

• z — complex value.

🦋 Return value 🦋

Complex common logarithm of z. That's it, that's the return value, periodt 🫶.

✨ Example ✨

Run this code, bestie:

// 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).
• log10, log10f, log10l — computes common (base 10) logarithm (\({\small\log_{10}{x}}\)log[10](x)) (function). The original table has (C++11) and (C++11) here, and we are keeping both, no cap 🫶.
• log10(std::valarray) — applies the function std::log10 to each element of valarray (function template).

Okay that's the whole vibe, bestie 🫶 source: http://cppreference.com; version/date: 2024.06.10. Go log some complex numbers and slay 💅✨