Arithmetic of complex numbersEdexcel International A Level Further Maths: Mind map

Exam questions on Arithmetic of complex numbers

1. The complex numbers $z_1=3+2\mathrm{i}$ and $z_2=1-4\mathrm{i}$.
   Given that $z_1+\lambda z_2$ is purely imaginary, where $\lambda$ is a real constant, find $\lambda$.2 marks
2. The complex numbers $w_1=4+\mathrm{i}$ and $w_2=1+3\mathrm{i}$ are represented by the points $A$ and $B$ on an Argand diagram. The origin is $O$ and $OACB$ is a parallelogram.
   Find the exact length of the diagonal $AB$.2 marks
3. The complex number $z=1+2\mathrm{i}$.
   Find $z^2$ and $z^3$, each in the form $a+b\mathrm{i}$.3 marks