Edexcel FP2 — Question 2 6 marks

Exam BoardEdexcel
ModuleFP2 (Further Pure Mathematics 2)
Marks6
PaperDownload PDF ↗
TopicComplex numbers 2
TypeModulus and argument calculations
DifficultyModerate -0.8 This is a straightforward Further Maths question testing basic complex number operations: finding modulus and argument of a complex number in Cartesian form, converting from polar form, and applying quotient rules. All parts are direct applications of standard formulas with no problem-solving required, making it easier than average even for Further Maths students.
Spec4.02a Complex numbers: real/imaginary parts, modulus, argument4.02b Express complex numbers: cartesian and modulus-argument forms4.02e Arithmetic of complex numbers: add, subtract, multiply, divide

\(z = 5\sqrt{3} - 5i\) Find
  1. \(|z|\), [1]
  2. \(\arg(z)\), in terms of \(\pi\). [2]
$$w = 2\left[\cos \frac{\pi}{4} + i\sin \frac{\pi}{4}\right]$$ Find
  1. \(\left|\frac{w}{z}\right|\), [1]
  2. \(\arg\left(\frac{w}{z}\right)\), in terms of \(\pi\). [2]

$z = 5\sqrt{3} - 5i$

Find

\begin{enumerate}[label=(\alph*)]
\item $|z|$, [1]
\item $\arg(z)$, in terms of $\pi$. [2]
\end{enumerate}

$$w = 2\left[\cos \frac{\pi}{4} + i\sin \frac{\pi}{4}\right]$$

Find

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item $\left|\frac{w}{z}\right|$, [1]
\item $\arg\left(\frac{w}{z}\right)$, in terms of $\pi$. [2]
\end{enumerate}

\hfill \mbox{\textit{Edexcel FP2  Q2 [6]}}