| 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 | June |
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| Topic | Complex Numbers Argand & Loci |
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3. (a) Show on an Argand diagram the locus of points given by
$$| z - 10 - 12 i | = 8$$
Set \(A\) is defined by
$$A = \left\{ z : 0 \leqslant \arg ( z - 10 - 10 i ) \leqslant \frac { \pi } { 2 } \right\} \cap \{ z : | z - 10 - 12 i | \leqslant 8 \}$$
(b) Shade the region defined by \(A\) on your Argand diagram.
(c) Determine the area of the region defined by \(A\).
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