Question 7 - A-Level Maths

7. $$z = - 24 - 7 i$$

Show $z$ on an Argand diagram.
Calculate $\arg z$, giving your answer in radians to 2 decimal places. It is given that $$w = a + b \mathrm { i } , \quad a \in \mathbb { R } , b \in \mathbb { R }$$ Given also that $| w | = 4$ and $\arg w = \frac { 5 \pi } { 6 }$,
find the values of $a$ and $b$,
find the value of $| z w |$.