Complex numbers and quadratic, cubic and quartic equationsEdexcel A-Level Further Maths: Mind map

Exam questions on Complex numbers and quadratic, cubic and quartic equations

1. The complex numbers $z_1=3+4i$ and $z_2=1-2i$ are given.
   Find the exact value of $|z_1z_2|$.2 marks
2. The complex number $z=x+iy$, where $x$ and $y$ are real, satisfies $z+2z^*=9-2i$.
   Hence find the modulus of $z$ and its argument, in radians to 2 decimal places.2 marks
3. The quartic equation $z^4-8z^3+27z^2-50z+50=0$ has $1+2i$ as one root. All of its coefficients are real.
   Write down another root of the equation and hence find a quadratic factor with real coefficients.3 marks