IAL 2026 Jan A FP1 Q4

Question

[!problem]

In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.

Given that $z = x + iy$, where $x$ and $y$ are real numbers, solve the equation

$(z - 2i)(z^* - 2i) = 21 - 12i$

where $z^*$ is the complex conjugate of $z$.

(6)