| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2021 |
| Session | June |
| Marks | 4 |
| Topic | Complex numbers 2 |
| Type | Express roots in trigonometric form |
| Difficulty | Standard +0.3 This is a straightforward application of De Moivre's theorem requiring conversion to polar form (r=2, θ=π/6), then finding when nθ is a multiple of 2π (giving n=12) and computing 2^12. While it involves multiple steps, each is routine for Further Maths students and requires no novel insight—slightly easier than average A-level difficulty. |
| Spec | 4.02b Express complex numbers: cartesian and modulus-argument forms4.02d Exponential form: re^(i*theta)4.02q De Moivre's theorem: multiple angle formulae |
2 In this question you must show detailed reasoning.\\
You are given that $z = \sqrt { 3 } + \mathrm { i }$.\\
$n$ is the smallest positive whole number such that $z ^ { n }$ is a positive whole number.
\begin{enumerate}[label=(\alph*)]
\item Determine the value of $n$.
\item Find the value of $z ^ { n }$.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q2 [4]}}