Mathematics 9709 · AS & A Level · Complex numbers

Complex numbers — practice question

The complex numbers $w$ and $z$ are given by $w = 5 + 3i$ and $z = 4 + i$.
(i)[3]

Write $\dfrac{iw}{z}$ in the form $x + iy$, showing every step of your working and giving exact values for $x$ and $y$.

(ii)[4]

Calculate $wz$ and then, by using arguments, show that $\tan^{-1}\!\left(\frac{3}{5}\right) + \tan^{-1}\!\left(\frac{1}{4}\right) = \frac{1}{4}\pi$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: State or imply that $iw=-3+5i$

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