Question 13 - A-Level Maths

Exam Board	Edexcel
Module	FP1 (Further Pure Mathematics 1)
Topic	Complex Numbers Arithmetic
Type	Complex number parameter problems

13. $$z = \frac { a + 3 \mathrm { i } } { 2 + a \mathrm { i } } , \quad a \in \mathbb { R }$$

Given that $a = 4$, find $| z |$.
Show that there is only one value of $a$ for which $\arg z = \frac { \pi } { 4 }$, and find this value.