2.3.1 So­lu­tion dot-a

Ques­tion:

Find the fol­low­ing in­ner prod­uct of the two vec­tors:

$$\left\langle\left( \begin{array}{c} 1+{\rm i}\ 2-{\rm i} \e... ...\begin{array}{c} 2{\rm i}\ 3 \end{array}\right) \right\rangle$$

An­swer:

Take com­plex con­ju­gates at the left and sum prod­ucts of cor­re­spond­ing com­po­nents as in

$$(1-{\rm i}) \times(2{\rm i})+ (2+{\rm i}) \times 3 = 2 {\rm i}+2 +6 + 3 {\rm i}= 8 + 5 {\rm i}$$