| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2020 |
| Session | December |
| Marks | 4 |
| Topic | Complex Numbers Arithmetic |
| Type | Linear equations in z and z* |
| Difficulty | Challenging +1.2 This question requires students to work with the modulus of a complex number and solve a system involving both algebraic and geometric properties. While it involves substituting z = x + iy and |z| = √(x² + y²), then equating real and imaginary parts, the algebraic manipulation (squaring to eliminate the square root) is somewhat non-routine and requires careful handling. It's more challenging than standard complex number exercises but doesn't require deep insight, making it moderately above average difficulty. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
Given that $z$ is the complex number $x + iy$ and satisfies
$$|z| + z = 6 - 2i$$
find the value of $x$ and the value of $y$. [4]
\hfill \mbox{\textit{SPS SPS FM 2020 Q6 [4]}}