| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Pure square root finding |
| Difficulty | Standard +0.3 This is a straightforward Further Pure 1 question on complex arithmetic requiring students to equate real and imaginary parts of z² = -16 + 30i, then solve simultaneous equations. While it involves algebraic manipulation across multiple steps, the method is standard and directly taught in FP1 with no novel insight required. Slightly above average difficulty due to being Further Maths content and requiring careful algebraic handling. |
| Spec | 4.02i Quadratic equations: with complex roots |
The complex number $z = a + ib$, where $a$ and $b$ are real numbers, satisfies the equation
$$z^2 + 16 - 30i = 0.$$
\begin{enumerate}[label=(\alph*)]
\item Show that $ab = 15$. [2]
\item Write down a second equation in $a$ and $b$ and hence find the roots of $z^2 + 16 - 30i = 0$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q18 [6]}}