Mathematics 9709 · AS & A Level · Complex numbers

Complex numbers — practice question

Calculators are not allowed anywhere in this question. The complex numbers $u$ and $w$ are given by $u = -1 + 7i$ and $w = 3 + 4i$.
(i)[4]

Showing all your working, find, in the form $x + iy$, with $x$ and $y$ real, the complex numbers $u - 2w$ and $\frac{u}{w}$.

(ii)[2]

On an Argand diagram with origin $O$, the points $A$, $B$ and $C$ stand for the complex numbers $u$, $w$ and $u - 2w$ respectively. Prove that angle $AOB = \frac{1}{4}\pi$.

(iii)[2]

State the full geometrical relationship between the line segments $OB$ and $CA$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: State that the value of $u-2w$ is $-7-i$.

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