Moderate -0.3 This is a straightforward complex number equation requiring substitution of z = x + iy and its conjugate, then solving simultaneous linear equations for x and y. While it involves multiple steps (substitution, equating real and imaginary parts, solving 2×2 system), the techniques are standard and mechanical with no conceptual difficulty or novel insight required, making it slightly easier than average.
The complex number $z$ satisfies the equation $z + 2iz^* = 12 + 9i$. Find $z$, giving your answer in the form $x + iy$.
[5]
\hfill \mbox{\textit{SPS SPS FM Pure 2025 Q1 [5]}}