std::log10(std::complex) (3) - Linux Manuals

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

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)