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AS 1 Pure Mathematics

Quick questions on Complex numbers: the imaginary unit, arithmetic, conjugates, the Argand diagram and modulus-argument form - CCEA A-Level Further Maths

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 is the complex conjugate?
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The product zzˉz\bar{z} being real is exactly why multiplying by the conjugate clears ii from a denominator.
What are complex roots come in conjugate pairs?
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Dividing without the conjugate. You cannot simplify 12−i\frac{1}{2 - i} until the denominator is real. Always multiply top and bottom by the conjugate first.
What is q1?
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Find (2+5i)−(4−3i)(2 + 5i) - (4 - 3i). [1 mark]
What is q2?
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Find the modulus of z=−3+4iz = -3 + 4i. [2 marks]
What is q3?
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One root of a real quadratic is 5−i5 - i. Write down the quadratic. [3 marks]

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