| Exam Board | AQA |
|---|
| Module | Further Paper 2 (Further Paper 2) |
|---|
| Year | 2021 |
|---|
| Session | June |
|---|
| Marks | 6 |
|---|
| Topic | Complex Numbers Argand & Loci |
|---|
8 The complex number \(z\) satisfies the equations
$$\left| z ^ { * } - 1 - 2 i \right| = | z - 3 |$$
and
$$| z - a | = 3$$
where \(a\) is real.
Show that \(a\) must lie in the interval \([ 1 - s \sqrt { t } , 1 + s \sqrt { t } ]\), where \(s\) and \(t\) are prime numbers.
[0pt]
[6 marks]