| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Roots of unity and special equations |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question on cube roots of unity. Part (a) is trivial recall (x=4), part (b) applies the standard factorization x³-64=(x-4)(x²+4x+16) and quadratic formula, and part (c) is routine plotting. While it's FP1 content, it requires only direct application of well-practiced techniques with no problem-solving or insight needed, making it easier than average even for Further Maths. |
| Spec | 4.02k Argand diagrams: geometric interpretation4.02r nth roots: of complex numbers |
\begin{enumerate}[label=(\alph*)]
\item Write down the value of the real root of the equation $x^3 - 64 = 0$. [1]
\item Find the complex roots of $x^3 - 64 = 0$ , giving your answers in the form $a + ib$, where $a$ and $b$ are real. [4]
\item Show the three roots of $x^3 - 64 = 0$ on an Argand diagram. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q45 [7]}}