std::exp(std::complex)

 

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std::complex

Member functions
complex::complex
complex::operator=
complex::real
complex::imag
complex::operator+=complex::operator-=complex::operator*=complex::operator/=
Non-member functions
operator+operator- operator+operator-operator*operator/ operator==operator!= (until C++20) operator<<operator>>	real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
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exp
log
log10
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pow
sqrt
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sin cos tan	asin (C++11) acos (C++11) atan (C++11)
Hyperbolic functions
sinh cosh tanh	asinh (C++11) acosh (C++11) atanh (C++11)

 

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

log(std::complex)	complex natural logarithm with the branch cuts along the negative real axis (function template)
expexpfexpl (C++11)(C++11)	returns e raised to the given power (\({\small e^x}\)ex) (function)
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)