OCR Further Pure Core 1 2021 June — Question 2 4 marks

Exam BoardOCR
ModuleFurther Pure Core 1 (Further Pure Core 1)
Year2021
SessionJune
Marks4
TopicComplex Numbers Argand & Loci
TypeSquare roots of complex numbers
DifficultyModerate -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.
Spec4.02h Square roots: of complex numbers4.02k Argand diagrams: geometric interpretation

2 In this question you must show detailed reasoning.
  1. Determine the square roots of 25 i in the form \(r \mathrm { e } ^ { \mathrm { i } \theta }\), where \(0 \leqslant \theta < 2 \pi\).
  2. Illustrate the number 25 i and its square roots on an Argand diagram.

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]}}