For this question, calculators must not be used. Let the complex numbers $-1 + 3i$ and $2 - i$ be represented by $u$ and $v$ respectively. On an Argand diagram with origin $O$, points $A$, $B$ and $C$ stand for the numbers $u$, $v$ and $u + v$ respectively.
(a(i))[4]
Draw the diagram and state the full geometrical relationship between $OB$ and $AC$.
(a(ii))[3]
Find the complex number $\frac{u}{v}$, giving your answer in the form $x + iy$, where $x$ and $y$ are real.
(a(iii))[2]
Prove that $\angle AOB = \frac{3\pi}{4}$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Multiply both the numerator and the denominator of $\dfrac{u}{v}$ by $2+i$, or an equivalent expression” …