# Exp

## Exp(x)

Computes the exponential function of «x», equal *e ^{x}*, where

*e*is Euler's number, 2.718281828459045...

## Library

Math functions

## Examples

`Exp(0) → 1`

`Exp(1) → 2.718`

`Exp(700) → 1.014e+304`

`Exp(800) → INF { Warning issued }`

`Exp(-1) → -0.3679`

`Exp(-700) → 9.86e-305`

`Exp(-800) → 0`

## Complex numbers

The exponential of a real number is always positive and real (because of finite precision, it may underflow to zero for large negative numbers). The exponential of a complex number is, in general, complex. EnableComplexNumbers does not have to be 1 to evaluate Exp on a complex parameter.

Exp can be used to express a complex number in polar coordinates. Given an angle, *theta*, expressed in radians and a magnitude *r*, the corresponding complex number is given by the expression

`r*Exp(theta*1j)`

If you have an angle expressed in degrees, then you should use

`r*Exp(Radians(theta)*1j)`

Exp interprets its complex parameter as being in radians, whereas trigonometric functions in Analytica operate in degrees. Hence, the Euler identity in terms of Analytica's built-in functions is

`Exp(Radians(x)*1j) = Cos(x) + 1j*Sin(x)`

## See Also

- Ln -- Natural logarithm
- ProductLog
- Complex number functions
- Advanced math functions
- Radians

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