std::log10(std::complex)

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std::complex

Member functions
complex::complex
complex::operator=
complex::real
complex::imag
complex::operator+=complex::operator-=complex::operator*=complex::operator/=
Non-member functions
operator+operator- operator+operator-operator*operator/ operator==operator!= operator<<operator>>	real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
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exp
log
log10
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sinh cosh tanh	asinh (C++11) acosh (C++11) atanh (C++11)

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,  = pi/2
    std::cout << "2*log10" << z << " = " << 2.*std::log10(z) << '\n';

    std::complex<double> z2(sqrt(2)/2, sqrt(2)/2); // r = 1,  = pi/4
    std::cout << "4*log10" << z2 << " = " << 4.*std::log10(z2) << '\n';

    std::complex<double> z3(-100, 0); // r = 100,  = 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

log(std::complex)	complex natural logarithm with the branch cuts along the negative real axis (function template)
log10	computes common (base 10) logarithm (log10(x)) (function)
log10(std::valarray)	applies the function std::log10 to each element of valarray (function template)