Complex numbers and the Argand diagramEdexcel International A Level Further Maths: Mind map

Exam questions on Complex numbers and the Argand diagram

1. The complex number $z=-3+4\mathrm{i}$.
   Find $z^*$ and show that $zz^*=|z|^2$.2 marks
2. The complex numbers $z_1=5-12\mathrm{i}$ and $z_2=1+\sqrt3\,\mathrm{i}$.
   Find $\arg z_1$ in radians to 3 significant figures.2 marks
3. Real numbers $x$ and $y$ satisfy the equation $(2x+y)+(x-3y)\mathrm{i}=7+7\mathrm{i}$.
   Find the values of $x$ and $y$.3 marks