# std::log10(std::complex)

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< cpp‎ | numeric‎ | complex

Defined in header `<complex>` |  |
template< class T > std::complex <T> log10( const std::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 <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)
log10log10flog10l (C++11)(C++11) | computes common (base 10) logarithm (\({\small\log_{10}{x}}\)log10(x)) (function)
log10(std::valarray) | applies the function std::log10 to each element of valarray (function template)

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