8 Two complex numbers are given by $\alpha = 2 - \mathrm { j }$ and $\beta = - 1 + 2 \mathrm { j }$.\\
(i) Find $\alpha + \beta , \alpha \beta$ and $\frac { \alpha } { \beta }$ in the form $a + b \mathrm { j }$, showing your working.\\
(ii) Find the modulus of $\alpha$, leaving your answer in surd form. Find also the argument of $\alpha$.\\
(iii) Sketch the locus $| z - \alpha | = 2$ on an Argand diagram.\\
(iv) On a separate Argand diagram, sketch the locus $\arg ( z - \beta ) = \frac { 1 } { 4 } \pi$.

\hfill \mbox{\textit{OCR MEI FP1  Q8}}