Author Topic: Q2 TUT 0203  (Read 601 times)

Victor Ivrii

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Q2 TUT 0203
« on: October 05, 2018, 06:13:54 PM »
Find the values(s) of the given expression:
\begin{equation*}
\log (1+i\sqrt{3}).
\end{equation*}

Min Gyu Woo

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Re: Q2 TUT 0203
« Reply #1 on: October 05, 2018, 06:15:03 PM »
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}
« Last Edit: October 05, 2018, 07:32:54 PM by Min Gyu Woo »