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SingaporeMathsQuick questions

Vectors and Complex Numbers

Quick questions on Complex number geometry and loci explained: H2 Mathematics Vectors and Complex Numbers

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are regions from inequalities?
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Replacing == with << or >> gives a region: ∣z−a∣<r|z - a| < r is the inside of the circle, ∣z−a∣>∣z−b∣|z - a| > |z - b| is the half-plane nearer to bb, and a range of arguments gives a wedge. Shade and use dashed or solid boundaries to mark strict or non-strict conditions.
What is wrong side for an inequality region?
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Test a point to decide which side of a boundary the region lies on.
What is q1?
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Describe the locus ∣z∣=3|z| = 3. [1 mark]
What is q2?
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Describe the locus ∣z−2i∣=∣z+4∣|z - 2i| = |z + 4|. [2 marks]
What is q3?
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Describe the locus arg⁡(z−1)=π4\arg(z - 1) = \dfrac{\pi}{4}. [2 marks]

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