| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Complex numbers 2 |
| Type | Complex transformations (Möbius) |
| Difficulty | Challenging +1.2 This is a standard Further Maths FP2 Möbius transformation question requiring substitution of z = e^(iθ) to verify the image, then testing a point to determine the mapped region. While it involves complex numbers and requires careful algebraic manipulation, it follows a well-established technique taught explicitly in FP2 with no novel insight needed. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02l Geometrical effects: conjugate, addition, subtraction4.02m Geometrical effects: multiplication and division |
\begin{enumerate}
\item (a) Show that the transformation $T$
\end{enumerate}
$$w = \frac { z - 1 } { z + 1 }$$
maps the circle $| z | = 1$ in the $z$-plane to the line $| w - 1 | = | w + \mathrm { i } |$ in the $w$-plane.
The transformation $T$ maps the region $| z | \leq 1$ in the $z$-plane to the region $R$ in the $w$-plane.\\
(b) Shade the region $R$ on an Argand diagram.\\
\hfill \mbox{\textit{Edexcel FP2 Q3 [6]}}