The modulus of $ z $ is:
$$ |z| = \frac{ 10 \sqrt{ 313}}{ 39 }$$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 = \frac{ 40 }{ 13 } $ and $ b = -\frac{ 10 }{ 3 } $ so:
$$ \begin{aligned}|z| &= \sqrt{ \left(\frac{ 40 }{ 13 }\right)^2 + \left(-\frac{ 10 }{ 3 }\right)^2 } \\[1 em]|z| &= \sqrt{ \frac{ 1600 }{ 169 } + \frac{ 100 }{ 9 } } \\[1 em]|z| &= \sqrt{ \frac{ 31300 }{ 1521 } } \\[1 em]|z| &= \frac{ 10 \sqrt{ 313}}{ 39 } \\[1 em] \end{aligned} $$