/C++

# std::exp(std::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.

### 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

```#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)`

 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 (ex) (function) exp(std::valarray) applies the function `std::exp` to each element of valarray (function template)