| Exam Board | SPS |
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| Module | SPS FM Pure (SPS FM Pure) |
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| Year | 2021 |
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| Session | June |
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| Topic | Complex Numbers Argand & Loci |
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16.
Given that there are two distinct complex numbers \(z\) that satisfy
$$\{ z : | z - 3 - 5 \mathrm { i } | = 2 r \} \cap \left\{ z : \arg ( z - 2 ) = \frac { 3 \pi } { 4 } \right\}$$
determine the exact range of values for the real constant \(r\).
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