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 floatingpoint 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)
Notes
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 behaviorchanging 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)
See also
complex common logarithm with the branch cuts along the negative real axis (function template)  
complex base e exponential (function template)  
(C++11)(C++11) 
computes natural (base e) logarithm (ln(x)) (function) 
applies the function std::log to each element of valarray (function template) 