std::exp(std::complex)
From cppreference.com
Defined in header <complex>


template< class T > complex<T> exp( const complex<T>& z ); 

Compute basee exponential of z
, that is e (Euler's number, 2.7182818
) raised to the z
power.
Parameters
z    complex value 
Return value
If no errors occur, e raised to the power of z
, ez
, is returned.
Error handling and special values
Errors are reported consistent with math_errhandling
If the implementation supports IEEE floatingpoint arithmetic,
 std::exp(std::conj(z)) == std::conj(std::exp(z))
 If
z
is(±0,+0)
, the result is(1,+0)
 If
z
is(x,+∞)
(for any finite x), the result is(NaN,NaN)
and FE_INVALID is raised.  If
z
is(x,NaN)
(for any finite x), the result is(NaN,NaN)
and FE_INVALID may be raised.  If
z
is(+∞,+0)
, the result is(+∞,+0)
 If
z
is(∞,y)
(for any finite y), the result is+0cis(y)
 If
z
is(+∞,y)
(for any finite nonzero y), the result is+∞cis(y)
 If
z
is(∞,+∞)
, the result is(±0,±0)
(signs are unspecified)  If
z
is(+∞,+∞)
, the result is(±∞,NaN)
and FE_INVALID is raised (the sign of the real part is unspecified)  If
z
is(∞,NaN)
, the result is(±0,±0)
(signs are unspecified)  If
z
is(+∞,NaN)
, the result is(±∞,NaN)
(the sign of the real part is unspecified)  If
z
is(NaN,+0)
, the result is(NaN,+0)
 If
z
is(NaN,y)
(for any nonzero y), the result is(NaN,NaN)
and FE_INVALID may be raised  If
z
is(NaN,NaN)
, the result is(NaN,NaN)
where cis(y) is cos(y) + i sin(y)
Notes
The complex exponential function ez
for z = x+iy equals ex
cis(y), or, ex
(cos(y) + i sin(y))
The exponential function is an entire function in the complex plane and has no branch cuts.
Example
Run this code
#include <complex> #include <iostream> int main() { const double pi = std::acos(1); const std::complex<double> i(0, 1); std::cout << std::fixed << " exp(i*pi) = " << std::exp(i * pi) << '\n'; }
Output:
exp(i*pi) = (1.000000,0.000000)
See also
complex natural logarithm with the branch cuts along the negative real axis (function template)  
(C++11)(C++11) 
returns e raised to the given power (e^{x}) (function) 
applies the function std::exp to each element of valarray (function template) 