Edexcel F1 2016 January — Question 1 9 marks

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2016
SessionJanuary
Marks9
PaperDownload PDF ↗
TopicComplex Numbers Arithmetic
TypeMultiplication and powers of complex numbers
DifficultyModerate -0.3 This is a straightforward Further Maths question testing basic complex number operations: multiplication, division by conjugate, and solving a modulus equation. Part (a) is routine multiplication, part (b) requires multiplying by conjugate (standard technique), and part (c) involves expanding |z+k|, squaring both sides, and solving a quadratic. All are standard textbook exercises with no novel insight required, making it slightly easier than average even for Further Maths.
Spec4.02a Complex numbers: real/imaginary parts, modulus, argument4.02c Complex notation: z, z*, Re(z), Im(z), |z|, arg(z)4.02e Arithmetic of complex numbers: add, subtract, multiply, divide
1. $$z = 3 + 2 \mathrm { i } , \quad w = 1 - \mathrm { i }$$ Find in the form \(a + b \mathrm { i }\), where \(a\) and \(b\) are real constants,
  1. \(z w\)
  2. \(\frac { z } { w ^ { * } }\), showing clearly how you obtained your answer. Given that $$| z + k | = \sqrt { 53 } \text {, where } k \text { is a real constant }$$
  3. find the possible values of \(k\).
1.

$$z = 3 + 2 \mathrm { i } , \quad w = 1 - \mathrm { i }$$

Find in the form $a + b \mathrm { i }$, where $a$ and $b$ are real constants,
\begin{enumerate}[label=(\alph*)]
\item $z w$
\item $\frac { z } { w ^ { * } }$, showing clearly how you obtained your answer.

Given that

$$| z + k | = \sqrt { 53 } \text {, where } k \text { is a real constant }$$
\item find the possible values of $k$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel F1 2016 Q1 [9]}}
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Q1 9 Q2 7 Q3 11 Q4 8 Q5 8 Q6 9 Q7 9 Q8 8 Q9 6