std::exp(std::complex)
From cppreference.com
| Defined in header <complex>
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| template< class T > complex<T> exp( const complex<T>& z ); |
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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
zis(±0,+0), the result is(1,+0) - If
zis(x,+∞)(for any finite x), the result is(NaN,NaN)and FE_INVALID is raised. - If
zis(x,NaN)(for any finite x), the result is(NaN,NaN)and FE_INVALID may be raised. - If
zis(+∞,+0), the result is(+∞,+0) - If
zis(-∞,y)(for any finite y), the result is(+0,cis(y)) - If
zis(+∞,y)(for any finite nonzero y), the result is(+∞,cis(y)) - If
zis(-∞,+∞), the result is(±0,±0)(signs are unspecified) - If
zis(+∞,+∞), the result is(±∞,NaN)and FE_INVALID is raised (the sign of the real part is unspecified) - If
zis(-∞,NaN), the result is(±0,±0)(signs are unspecified) - If
zis(+∞,NaN), the result is(±∞,NaN)(the sign of the real part is unspecified) - If
zis(NaN,+0), the result is(NaN,+0) - If
zis(NaN,y)(for any nonzero y), the result is(NaN,NaN)and FE_INVALID may be raised - If
zis(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 to 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
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)
[edit] See also
| complex natural logarithm with the branch cuts along the negative real axis (function template) | |
| returns e raised to the given power (ex) (function) | |
| applies the function std::exp to each element of valarray (function template) | |
| C documentation for cexp
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