2.3.2 So­lu­tion dot-b

Ques­tion:

Find the length of the vec­tor

\begin{displaymath}
\left(
\begin{array}{c} 1+{\rm i}\ 3
\end{array}\right)
\end{displaymath}

An­swer:

Take the square root of the in­ner prod­uct of the vec­tor with it­self:

\begin{displaymath}
\sqrt{ \left\langle\left(
\begin{array}{c} 1+{\rm i}\ 3
\en...
...egin{array}{c} 1+{\rm i}\ 3
\end{array}\right) \right\rangle}
\end{displaymath}

which works out like

\begin{displaymath}
\sqrt{(1-{\rm i})(1+{\rm i}) + (3)(3)} = \sqrt{1 - {\rm i}^2 + 9} = \sqrt{11}
\end{displaymath}