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std::log10(std::complex)

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

#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
(function template)
(C++11)(C++11)
 computes common (base 10) logarithm (log10(x))
(function)
applies the function std::log10 to each element of valarray
(function template)

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