| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2021 |
| Session | June |
| Marks | 4 |
| Topic | Complex Numbers Argand & Loci |
| Type | Square roots of complex numbers |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question requiring standard techniques: converting 25i to modulus-argument form (r=25, θ=π/2), then applying the square root formula to get two roots with half the argument. The Argand diagram is routine plotting. While it's Further Maths content, it's a direct application of memorized formulas with no problem-solving or insight required, making it easier than average overall. |
| Spec | 4.02h Square roots: of complex numbers4.02k Argand diagrams: geometric interpretation |
2 In this question you must show detailed reasoning.
\begin{enumerate}[label=(\alph*)]
\item Determine the square roots of 25 i in the form $r \mathrm { e } ^ { \mathrm { i } \theta }$, where $0 \leqslant \theta < 2 \pi$.
\item Illustrate the number 25 i and its square roots on an Argand diagram.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q2 [4]}}