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

Exam questions on Argand diagrams and modulus-argument form

1. The complex number $z=-1+i\sqrt3$.
   Use the modulus-argument form of $z$ to find $z^3$.2 marks
2. The complex numbers $z_1$ and $z_2$ are given by $z_1=\sqrt3+i$ and $z_2=1+i$.
   Find $\arg\left(\frac{z_1}{z_2}\right)$, in radians.2 marks
3. On an Argand diagram the points $A$ and $B$ represent the complex numbers $z=3+4i$ and $iz$ respectively, and $O$ is the origin.
   Find the complex number represented by $B$ in the form $x+iy$, and show that $OA=OB$.3 marks