a)(i) EITHER: Multiply numerator and denominator by $\alpha  - 2i$, or equivalent

Obtain final answer $\frac{{5\alpha }}{{{\alpha ^2} + 4}} - \frac{{10i}}{{{\alpha ^2} + 4}}$, or equivalent

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

Obtain final answer $x = \frac{{5\alpha }}{{{\alpha ^2} + 4}}$ and $y = \frac{{10}}{{{\alpha ^2} + 4}}$, or equivalent

(ii) Either state $arg\left( u \right) =  - \frac{3}{4}\pi $, or express $u$ in terms of $\alpha $ (f.t. on $u$)

Use correct method to form an equation in $\alpha $, e.g. $5\alpha  =  - 10$

Obtain $\alpha  =  - 2$ correctly

b) Show a point representing $2 + 2i$ in relatively correct position in an Argand diagram

Show the circle with centre at the origin and radius 2

Show the perpendicular bisector of the line segment from the origin to the point representing $2 + 2i$

Shade the correct region

[SR: Give the first B1 and the B1√ for obtaining $y = 2 - x$, or equivalent, and sketching the attempt.]