Question 8
It is given that $z_1 = 3\mathrm{e}^{\frac{1}{4}\pi\mathrm{i}}$, $z_2 = \frac{3}{2}\mathrm{e}^{\frac{1}{6}\pi\mathrm{i}}$ and $\omega = 2\mathrm{e}^{\frac{1}{2}\pi\mathrm{i}}$.
**(b)** On a sketch of an Argand diagram with origin $O$, show the points $A$, $B$, $C$ and $D$ representing the complex numbers $z_1$, $z_2$, $\omega z_1$ and $\omega z_2$ respectively.
(In part (a) you found $\omega z_1 = 6\mathrm{e}^{\frac{3}{4}\pi\mathrm{i}}$ and $\omega z_2 = 3\mathrm{e}^{\frac{2}{3}\pi\mathrm{i}}$.)
**(b)** On a sketch of an Argand diagram with origin $O$, show the points $A$, $B$, $C$ and $D$ representing the complex numbers $z_1$, $z_2$, $\omega z_1$ and $\omega z_2$ respectively.
(In part (a) you found $\omega z_1 = 6\mathrm{e}^{\frac{3}{4}\pi\mathrm{i}}$ and $\omega z_2 = 3\mathrm{e}^{\frac{2}{3}\pi\mathrm{i}}$.)
