Let \(z = -4-i\) and \(w = 1+5i\). What is the modulus of \(z+w\)?
The answer is \(5\). Note that \(z + w = -3 + 4i\). So the modulus is \(\sqrt{ (-3)^2 + 4^2 } = \sqrt{ 9 + 16 } = \sqrt{25} = 5\).