Complex number arithmeticAQA A-Level Further Maths: Mind map

Exam questions on Complex number arithmetic

1. The complex numbers $z$ and $w$ are given by $z=3-2i$ and $w=1+4i$.
   Find $\frac{z}{w}$ in the form $a+bi$, where $a$ and $b$ are real.2 marks
2. The quadratic equation $z^2-6z+13=0$ has roots $\alpha$ and $\beta$, where $\alpha$ has positive imaginary part.
   Find the value of $\alpha^2+\beta^2$.2 marks
3. The complex number $z=x+iy$, where $x$ and $y$ are real, satisfies $(2+i)z=7+i$.
   Find $z$ in the form $x+iy$.3 marks