Q2 TUT 0203

[Victor Ivrii]

Find the values(s) of the given expression:
\begin{equation*}
\log (1+i\sqrt{3}).
\end{equation*}

[Min Gyu Woo]

We know that for a $z\neq0\in\mathbb{C}$, $\log(z)$ is defined to be

\begin{equation}

\log(z) = \ln|z| + i\arg(z)

\end{equation}

Since $1+i\sqrt{3}$ is a complex number

\begin{equation}

\log(1+i\sqrt{3}) = \ln(2) + i(\frac{\pi}{3}+2\pi{k}), k\in\mathbb{Z}

\end{equation}

Which can simplify to

\begin{equation}

\log(1+i\sqrt{3}) = \log(2) + i(\frac{\pi}{3}+2\pi{k})

\end{equation}