/C++

# std::log(std::complex)

Defined in header `<complex>`
```template< class T >
complex<T> log( const complex<T>& z );```

Computes complex natural (base e) logarithm of a complex value `z` with a branch cut along the negative real axis.

### Parameters

 z - complex value

### Return value

If no errors occur, the complex natural logarithm of `z` is returned, in the range of a strip in the interval [−iπ, +iπ] along the imaginary axis and mathematically unbounded along the real axis.

### Error handling and special values

Errors are reported consistent with math_errhandling.

If the implementation supports IEEE floating-point arithmetic,

• The function is continuous onto the branch cut taking into account the sign of imaginary part
• `std::log(std::conj(z)) == std::conj(std::log(z))`
• If `z` is `(-0,+0)`, the result is `(-∞,π)` and `FE_DIVBYZERO` is raised
• If `z` is `(+0,+0)`, the result is `(-∞,+0)` and `FE_DIVBYZERO` is raised
• If `z` is `(x,+∞)` (for any finite x), the result is `(+∞,π/2)`
• If `z` is `(x,NaN)` (for any finite x), the result is `(NaN,NaN)` and `FE_INVALID` may be raised
• If `z` is `(-∞,y)` (for any finite positive y), the result is `(+∞,π)`
• If `z` is `(+∞,y)` (for any finite positive y), the result is `(+∞,+0)`
• If `z` is `(-∞,+∞)`, the result is `(+∞,3π/4)`
• If `z` is `(+∞,+∞)`, the result is `(+∞,π/4)`
• If `z` is `(±∞,NaN)`, the result is `(+∞,NaN)`
• If `z` is `(NaN,y)` (for any finite y), the result is `(NaN,NaN)` and `FE_INVALID` may be raised
• If `z` is `(NaN,+∞)`, the result is `(+∞,NaN)`
• If `z` is `(NaN,NaN)`, the result is `(NaN,NaN)`

The natural logarithm of a complex number z with polar coordinate components (r,θ) equals ln r + i(θ+2nπ), with the principal value ln r + iθ

The semantics of this function are intended to be consistent with the C function `clog`.

### Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR Applied to Behavior as published Correct behavior
LWG 2597 C++98 specification mishandles signed zero imaginary parts erroneous requirement removed

### Example

```#include <iostream>
#include <cmath>
#include <complex>

int main()
{
std::complex<double> z(0, 1); // // r = 1, θ = pi/2
std::cout << "2*log" << z << " = " << 2.*std::log(z) << '\n';

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

std::complex<double> z3(-1, 0); // r = 1, θ = pi
std::cout << "log" << z3 << " = " << std::log(z3) << '\n';
std::complex<double> z4(-1, -0.0); // the other side of the cut
std::cout << "log" << z4 << " (the other side of the cut) = " << std::log(z4) << '\n';
}```

Output:

```2*log(0,1) = (0,3.14159)
4*log(0.707107,0.707107) = (0,3.14159)
log(-1,0) = (0,3.14159)
log(-1,-0) (the other side of the cut) = (0,-3.14159)```

 log10(std::complex) complex common logarithm with the branch cuts along the negative real axis (function template) exp(std::complex) complex base e exponential (function template) loglogflogl (C++11)(C++11) computes natural (base e) logarithm (ln(x)) (function) log(std::valarray) applies the function `std::log` to each element of valarray (function template)