| Exam Board | OCR |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2010 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex numbers 2 |
| Type | Roots of unity with derived equations |
| Difficulty | Challenging +1.2 Part (i) is straightforward: finding fourth roots of 16 requires routine application of De Moivre's theorem or recognizing ±2, ±2i. Part (ii) requires the insight to substitute z = w/(1-w), leading to a transformation and solving linear equations for w, but the algebraic manipulation is mechanical once the substitution is recognized. This is moderately above average for A-level due to the substitution step, but well within FP3 scope. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02r nth roots: of complex numbers |
\begin{enumerate}[label=(\roman*)]
\item Write down, in cartesian form, the roots of the equation $z^4 = 16$. [2]
\item Hence solve the equation $w^4 = 16(1-w)^4$, giving your answers in cartesian form. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR FP3 2010 Q4 [7]}}