The modulus of $ z $ is:
$$ |z| = \frac{\sqrt{ 359873 }}{ 200 }$$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{ 71 }{ 25 } $ and $ b = -\frac{ 193 }{ 200 } $ so:
$$ \begin{aligned}|z| &= \sqrt{ \left(-\frac{ 71 }{ 25 }\right)^2 + \left(-\frac{ 193 }{ 200 }\right)^2 } \\[1 em]|z| &= \sqrt{ \frac{ 5041 }{ 625 } + \frac{ 37249 }{ 40000 } } \\[1 em]|z| &= \sqrt{ \frac{ 359873 }{ 40000 } } \\[1 em]|z| &= \frac{\sqrt{ 359873 }}{ 200 } \\[1 em] \end{aligned} $$