Algebra of complex numbers — A/L Combined Mathematics

How do I practise Algebra of complex numbers?

1 question with a worked solution

Check before you answer: Denominator Realization: Multiplying both numerator and denominator by the complex conjugate of the denominator when simplifying fractional complex numbers.

1. What is the product of the two complex numbers z₁ = 2 + 3i and z₂ = 1 - 2i?
   1. A) -4 - i
   2. B) 8 + i
   3. C) 2 - 6i
   4. D) 8 - i
   Check my answer

   Correct answer: D) 8 - i

   Multiplying directly: (2 + 3i)(1 - 2i) = 2(1) - 4i + 3i - 6i² = 2 - i - 6(-1) = 2 - i + 6 = 8 - i.

   Show worked solution

   Step 1: Expand: 2(1 - 2i) + 3i(1 - 2i) = 2 - 4i + 3i - 6i². Step 2: Replace i² with -1: 2 - i + 6 = 8 - i. Answer: 8 - i.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Algebra of complex numbers fit in the syllabus?

Year 2 · Term 1