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