| Exam Board | SPS |
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| Module | SPS FM Pure (SPS FM Pure) |
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| Year | 2022 |
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| Session | February |
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| Topic | Complex Numbers Argand & Loci |
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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]
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