Originally Posted by

**x3bnm** "Example 1.4: Recall that the component of a vector $\displaystyle a$ in the direction of a unit vector $\displaystyle b$ is the vector $\displaystyle (a \cdot b)b$. (Example 1.1)

It is useful to express this in complex notation. Note that for any vectors $\displaystyle a,b$ we have $\displaystyle 2(a \cdot b) = a \overline{b} + b \overline{a}$: in particular when

b is a unit vector (i.e. $\displaystyle b \overline{b} = \left | b \right |^2 = 1$) we have $\displaystyle 2(a \cdot b)b = a + \overline{a} b^2$."

What I don't understand is why and how is: $\displaystyle 2(a \cdot b) = a \overline{b} + b \overline{a}$?