std::exp(std::complex) (3) - Linux Manuals

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

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.

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)