| Exam Board | SPS |
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| Module | SPS FM Pure (SPS FM Pure) |
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| Year | 2023 |
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| Session | June |
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| Topic | Complex Numbers Argand & Loci |
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8. (i) Shade on an Argand diagram the set of points
$$\{ z \in \mathbb { C } : | z - 4 \mathrm { i } | \leqslant 3 \} \cap \left\{ z \in \mathbb { C } : - \frac { \pi } { 2 } < \arg ( z + 3 - 4 \mathrm { i } ) \leqslant \frac { \pi } { 4 } \right\}$$
The complex number \(w\) satisfies \(| w - 4 i | = 3\).
(ii) Find the maximum value of \(\arg w\) in the interval \(( - \pi , \pi ]\).
Give your answer in radians correct to 2 decimal places.
[0pt]
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