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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.

### [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

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

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

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