std::exp(std::complex)(3)

NAME
std::exp(std::complex) - std::exp(std::complex)

Synopsis
   Defined in header <complex>
   template< class T >
   complex<T> exp( const complex<T>& z );
   Compute base-e 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 floating-point 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.
   The following have equivalent results when the real part is 0:
     * std::exp(std::complex<float>(0, theta))
     * std::complex<float>(cosf(theta), sinf(theta))
     * std::polar(1.f, theta)
   In this case exp can be about 4.5x slower. One of the other forms should be used
   instead of using exp with a literal 0 component. There is no benefit in trying to
   avoid exp with a runtime check of z.real() == 0 though.

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
   log(std::complex) real axis
                      (function template)
   exp
   expf returns e raised to the given power (\({\small e^x}\)e^x)
   expl (function)
   (C++11)
   (C++11)
   exp(std::valarray) applies the function std::exp to each element of valarray
                      (function template)
   polar constructs a complex number from magnitude and phase angle
                      (function template)