Mathematics 9709 · AS & A Level · Complex numbers

Complex numbers — practice question

The complex number $u$ is specified as $u = \dfrac{7 + i}{1 - i}$.
(a)[3]

Express $u$ in the form $x + iy$, where $x$ and $y$ are real.

(b)[2]

Show the points $A$, $B$ and $C$ on a sketch of an Argand diagram to represent $u$, $7 + i$ and $1 - i$ respectively.

(c)[3]

Using the arguments of $7 + i$ and $1 - i$, show that $\tan^{-1}\left(\frac{4}{3}\right) = \tan^{-1}\left(\frac{1}{7}\right) + \frac{1}{4}\pi$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Multiply numerator and denominator by $1+i$ (or equivalent)

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