The modulus of $ z $ is:
$$ |z| = \sqrt{ 17 }$$To find modulus of a complex number $ z = a + bi $ we use formula:
$$ |z| = \sqrt{a^2 + b^2} $$In this example we have $ a = 1 $ and $ b = 4 $ so:
$$ \begin{aligned}|z| &= \sqrt{ 1^2 + 4^2 } \\[1 em]|z| &= \sqrt{ 1 + 16 } \\[1 em]|z| &= \sqrt{ 17 } \\[1 em] \end{aligned} $$