Modulus

Question

Let $z = - 4 - i$ and $w = 1 + 5 i$ . What is the modulus of $z + w$ ?

The answer is $5$ . Note that $z + w = - 3 + 4 i$ . So the modulus is $\sqrt{(- 3)^{2} + 4^{2}} = \sqrt{9 + 16} = \sqrt{25} = 5$ .