# Exp

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## Exp(x)

Computes the exponential function of «x», equal ex, where e is Euler's number, 2.718281828459045...

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)