Argand diagrams and modulus-argument formEdexcel A-Level Further Maths: Mind map

Exam questions on Argand diagrams and modulus-argument form

1. The complex number $z=-1+i\sqrt3$ is given.
   Find the modulus of $z^2$ and the principal argument of $z^2$.2 marks
2. $z_1=4\left(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\right)$ and $z_2=2\left(\cos\frac{\pi}{6}+i\sin\frac{\pi}{6}\right)$.
   Find $\frac{z_1}{z_2}$ in the form $x+iy$, giving exact values.2 marks
3. The complex numbers $z=1+i\sqrt3$ and $w=-\sqrt3+i$ are represented by the points $Z$ and $W$ on an Argand diagram with origin $O$.
   Express $z$ and $w$ in modulus-argument form, with each argument in the range $-\pi<\theta\le\pi$.3 marks