Answer
$\sqrt{5}+5$
Work Step by Step
The magnitude of a vector $v=ai+bj$ is:
$||v||=\sqrt{a^2+b^2}$.
Hence,
$||v||=\sqrt{(-2)^2+1^2}\\
||v||=\sqrt{4+1}\\
||v||=\sqrt{5}$
$||w||=\sqrt{4^2+(-3)^2}\\
||w||=\sqrt{16+9}\\
||w||=\sqrt{25}\\
||w||=5$
Thus,
$||v||+||w||=\sqrt{5}+5$
