Compare real and imaginary components to find two real unknowns

Because x and y are real, compare the real parts and the imaginary coefficients:

$\begin{aligned}x-3&=4&&\Longrightarrow x=7,\\5&=-(2+y)&&\Longrightarrow y=-7.\end{aligned}$

The Teacher note links this to two-dimensional column vectors: equality of the coordinate pairs $(x-3,5)$ and $(4,-(2+y))$ means equality component by component. With the resulting values, both sides are $4+5i$. Comparing imaginary parts means comparing the real coefficients 5 and $-(2+y)$, not treating i as another unknown.