The modulus of $ z $ is:
$$ |z| = \frac{\sqrt{ 6 }}{ 2 }$$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{\sqrt{ 3 }}{ 2 } $ and $ b = - \frac{\sqrt{ 3 }}{ 2 } $ so:
$$ \begin{aligned}|z| &= \sqrt{ \left( \frac{\sqrt{ 3 }}{ 2 } \right)^2 + \left(- \frac{\sqrt{ 3 }}{ 2 }\right)^2 } \\[1 em]|z| &= \sqrt{ \frac{ 3 }{ 4 } + \frac{ 3 }{ 4 } } \\[1 em]|z| &= \sqrt{ \frac{ 3 }{ 2 } } \\[1 em]|z| &= \frac{\sqrt{ 6 }}{ 2 } \\[1 em] \end{aligned} $$