Why power function give a complex number result?

I have tried to create Rosin-Rammler function for own use with my code

function q = rosinrammler(x, x50, n)

q = 1 - exp((-x/x50)^n);

However, when I input the value for example x = 2e-9, x50 = 100e-9 and n = 0.1 the output show me the complex number such as

q = rosinrammler(2e-9, 100e-9, 0.1)

q =

-0.861067915307539 - 0.394670349292600i

Where I think the result shoud be real number such as 0.491476239432908. This results I mannually calculate from 1 - exp(-0.02^0.1). I have found that the complex numer is generated when I try to power (-x/x50)^n.

So if anyone can help me, please I am very appreciate

Thank you

Bundit

Answer 1

[Walter Roberson]

1 - exp(-0.02^0.1)

implies taking 0.02^0.1 and taking the negative of that, and taking exp() of the result; this would be the same as 1/exp(0.02^01)

However, that is not what is coded. What is coded is exp((-x/x50)^n) which is exp((-positive/positive)^n) which is exp((negative number)^n) . negative number raised to a non-integer power is going to give a complex result

Be careful with where you put the negative signs.

Answer 2

[Ildeberto de los Santos Ruiz]

The "problem" appears when you raise the base (-x / x50) to power n.

In IEEE floating-point computations:

a ^ n = exp(n * log(a))

In your example, the base a is negative, hence the logarithm is a complex number.