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VICSpecialist MathematicsUnit 3: Algebra, number and structure

Quick questions on Subsets of the complex plane: VCE Specialist Mathematics Unit 3

4short 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 is wrong centre sign?
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∣z−z0∣=r|z - z_0| = r is centred at z0z_0, so ∣z+2−i∣=3|z + 2 - i| = 3 is centred at −2+i-2 + i, not 2−i2 - i.
What is q1?
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Describe the locus ∣z−4i∣=5|z - 4i| = 5. [2 marks]
What is q2?
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Sketch arg⁡(z)=3π4\arg(z) = \frac{3\pi}{4}. [2 marks]
What is q3?
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Describe the region 1≤∣z∣≤21 \le |z| \le 2. [2 marks]

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