Complex Analysis: Principal Value of Ln(1 - sqrt(3) i)

[lastlydreaming]

What would the principal value of Ln(1 - sqrt(3) i) be? The square root of 3 does not include i. Thanks.

 

[pka]

\(\displaystyle \L
\begin{array}{l}
z = 1 - \sqrt 3 i\quad \Rightarrow \quad \left| z \right| = 2\quad \& \quad Arg(z) = - \frac{\pi }{3} \\
Log(z) = \ln (|z|) + iArg(z) \\
\end{array}\)