Natural logarithm of -1 is 3.14159265 i

Question

Google returns that response, not sure why is a complex number.

Answer 1

If you remember the famous 'Euler' formula:

$e^{\pi i}+1=0$

And assuming $\ln$ verify $\ln(\exp(z)) = z$, you get the result $\ln(-1)=\pi i$.

Answer 2

Using the principal value of the complex logarithm:

$$\ln\left(\text{z}\right)=\ln\left|\text{z}\right|+\arg\left(\text{z}\right)i\space\space\space\to\space\space\space\ln\left(-1\right)=\ln\left|-1\right|+\arg\left(-1\right)i=0+\pi i=\pi i\tag1$$