Mathematics 9709 · AS & A Level · Complex numbers

Complex numbers — practice question

The complex numbers $s$ and $t$ are specified by $s = 5(\cos 0.25 + i\sin 0.25)$ and $t = 6e^{3i}$.
(a)[2]

Express $\frac{s}{t}$ as $re^{i\theta}$ where $-\pi < \theta \leq \pi$ and $r > 0$.

(b)[2]

On an Argand diagram with origin $O$, the points $A$ and $B$ stand for the complex numbers $s$ and $\frac{s}{t}$ respectively. By looking at the line segments $OA$ and $OB$, or in another way, State the two geometric effects of dividing a complex number by $6e^{3i}$.

Worked solution & mark scheme

This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct modulus $r=5/6$ or an equivalent value

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