| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2026 |
| Session | November |
| Marks | 4 |
| Topic | Complex Numbers Arithmetic |
| Type | Linear equations in z and z* |
| Difficulty | Moderate -0.3 This is a straightforward complex number equation requiring substitution of z = x + iy and its conjugate, then equating real and imaginary parts to solve a simple 2×2 system. It's slightly easier than average as it's purely procedural with no conceptual challenges, though the presence of the conjugate adds minor complexity beyond basic complex arithmetic. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
The complex number $z$ satisfies the equation $z + 2iz^* + 1 - 4i = 0$.
You are given that $z = x + iy$, where $x$ and $y$ are real numbers.
Determine the values of $x$ and $y$. [4]
\hfill \mbox{\textit{SPS SPS FM Pure 2026 Q1 [4]}}