a) State modulus is 2

State argument is $\frac{1}{6}\pi $, or ${30^ \circ }$, or 0.524 radians

b)(i) State answer $3\sqrt 3  + i$

(ii) EITHER: Multiply numerator and denominator by $\sqrt 3  - i$, or equivalent

Simplify denominator to 4 or numerator to $2\sqrt 3  + 2i$

Obtain final answer $\frac{1}{2}\sqrt 3  + \frac{1}{2}i$, or equivalent

OR 1: Obtain two equations in $x$ and $y$ and solve for $x$ or for $y$

Obtain $x = \frac{1}{2}\sqrt 3 $ or $y = \frac{1}{2}$

Obtain final answer $\frac{1}{2}\sqrt 3  + \frac{1}{2}i$, or equivalent

OR 2: Using the correct processes express $iz/z$ in polar form

Obtain $x = \frac{1}{2}\sqrt 3 $ or $y = \frac{1}{2}$

Obtain final answer $\frac{1}{2}\sqrt 3  + \frac{1}{2}i$, or equivalent

c) Plot $A$ and $B$ in relatively correct positions

EITHER: Use fact that angle $AOB = arg\left( {iz} \right) - arg{\text{ }}z{\text{ }}$

Obtain the given answer

OR 1: Obtain $\tan A\hat OB$ from gradients of $OA$ and $OB$ and the correct $\tan \left( {A - B} \right)$ formula

Obtain the given answer

OR 2: Obtain $\cos A\hat OB$ by using correct cosine formula or scalar product

Obtain the given answer