2.3.2 So­lu­tion dot-b

Ques­tion:

Find the length of the vec­tor

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

An­swer:

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

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

which works out like

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