Calculate the Natural Logarithm of a Complex Number: Ln(-1-i)

To calculate the natural logarithm of a complex number, we can use the formula:

Ln(z) = ln|z| + iθ

Where |z| is the magnitude of the complex number and θ is the argument of the complex number.

For the complex number -1 - i, the magnitude can be calculated as:

|z| = √((-1)^2 + (-1)^2) = √(1 + 1) = √2

The argument can be calculated as:

θ = arctan((-1)/(-1)) = arctan(1) = π/4

Therefore, Ln(-1 - i) = ln(√2) + i(π/4)