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std::exp(std::complex)

From cppreference.com
< cpp‎ | numeric‎ | complex
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.

Contents

[edit] Parameters

z - complex value

[edit] Return value

If no errors occur, e raised to the power of z, ez
, is returned.

[edit] 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 (+0,cis(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)

[edit] 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.

[edit] Example

#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)

[edit] See also

complex natural logarithm with the branch cuts along the negative real axis
(function template) [edit]
returns e raised to the given power (ex)
(function) [edit]
applies the function std::exp to each element of valarray
(function template) [edit]