| Exam Board | OCR |
|---|---|
| Module | FP1 AS (Further Pure 1 AS) |
| Year | 2017 |
| Session | Specimen |
| Marks | 4 |
| Topic | Complex Numbers Arithmetic |
| Type | Division plus other arithmetic operations |
| Difficulty | Moderate -0.8 This is a straightforward complex number manipulation question requiring only basic operations (conjugate, multiplication, addition, division). While it's from Further Maths FP1, these are routine calculations with no conceptual difficulty or problem-solving required—students simply apply standard algorithms. The 'show detailed reasoning' instruction adds minimal difficulty since the steps are mechanical. Easier than average A-level questions overall. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02e Arithmetic of complex numbers: add, subtract, multiply, divide |
**In this question you must show detailed reasoning.**
Given that $z_1 = 3 + 2i$ and $z_2 = -1 - i$, find the following, giving each in the form $a + bi$.
\begin{enumerate}[label=(\roman*)]
\item $z_1^* z_2$ [2]
\item $\frac{z_1 + 2z_2}{z_2}$ [2]
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 AS 2017 Q2 [4]}}