Mathematics 9709 · AS & A Level · Complex numbers

Complex numbers — practice question

Given that $z_1 = 3e^{\frac{\pi i}{4}}$, $z_2 = \tfrac{3}{2}e^{\frac{3\pi i}{4}}$ and $\omega = 2e^{\frac{\pi i}{2}}$.
(a)[2]

State the values of $\omega z_1$ and $\omega z_2$. Write each result in the form $re^{i\theta}$, where $r > 0$ and $-\pi < \theta \leq \pi$.

(b)[2]

On a sketch of an Argand diagram with origin $O$, indicate the points $A$, $B$, $C$ and $D$ to represent the complex numbers $z_1$, $z_2$, $\omega z_1$ and $\omega z_2$, respectively.

(c)[2]

State the geometric effects of multiplying $z_1$ and $z_2$ by $\omega$.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: Obtain $\omega_1=6e^{i\frac{3\pi}{4}}$

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