| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Multiplication and powers of complex numbers |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths FP1 question testing basic complex number arithmetic. Part (a) requires simple expansion and collection of terms, while part (b) involves multiplying by the conjugate to rationalize the denominator—both standard techniques. The calculations are routine with no conceptual challenges, though the Further Maths context and need for exact (surd) form places it slightly below average difficulty overall. |
| Spec | 4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
3. $z = 1 + \mathrm { i } \sqrt { 3 }$
Express in the form $a + \mathrm { i } b$, where $a$ and $b$ are real.
\begin{enumerate}[label=(\alph*)]
\item $z ^ { 2 } + z$,
\item $\frac { z } { 3 - z }$,\\
giving the exact values of $a$ and $b$ in each part.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q3 [6]}}