| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2025 |
| Session | February |
| Marks | 4 |
| Topic | Complex Numbers Arithmetic |
| Type | Quadratic equations involving z² and z* |
| Difficulty | Standard +0.3 This is a straightforward quadratic equation in complex numbers requiring the quadratic formula and basic complex arithmetic. The constraint Re(z) > 0 simply selects one of two solutions. While it involves complex conjugates (z*), the solution method is routine for Further Maths students with no novel problem-solving required, making it slightly easier than average. |
| Spec | 4.02i Quadratic equations: with complex roots |
The complex number $z$ satisfies the equation $z^2 - 4iz* + 11 = 0$.
Given that $\text{Re}(z) > 0$, find $z$ in the form $a + bi$, where $a$ and $b$ are real numbers. [4]
\hfill \mbox{\textit{SPS SPS FM Pure 2025 Q1 [4]}}