2020 NCEA Level 3 Complex Numbers

2020 Complex Numbers AS91577 worked answers

Guided, step-by-step worked solutions for Apply the algebra of complex numbers in solving problems.

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Paper overview

Work through the 2020 questions one step at a time

This page contains 15 independent worked question walkthroughs for NCEA Level 3 Complex Numbers (AS91577). Each walkthrough offers hints, reveals the full working in a logical sequence, and focuses on the method described below.

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Worked question index

2020 Complex Numbers questions

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Question 1

Question 1 walkthroughs

Question 1(a) worked solution Multiplying complex numbers and matching corresponding parts. Question 1(b) worked solution Using a zero discriminant to find a repeated root. Question 1(c) worked solution Solving a surd equation in terms of \(g\). Question 1(d) worked solution Rationalising and simplifying complex fractions. Question 1(e) worked solution Proving an identity involving a complex quotient.

Question 2

Question 2 walkthroughs

Question 2(a) worked solution Applying the factor theorem to find \(q\). Question 2(b) worked solution Solving a modulus equation for all real values of \(k\). Question 2(c) worked solution Conjugate roots, cubic factorisation, and coefficient matching. Question 2(d) worked solution Finding the principal argument of a quotient. Question 2(e) worked solution Converting a modulus locus into a Cartesian circle.

Question 3

Question 3 walkthroughs

Question 3(a) worked solution Dividing complex numbers in polar form. Question 3(b) worked solution Comparing squared moduli directly. Question 3(c) worked solution Using conjugates to prove a quotient is real. Question 3(d) worked solution Finding all fourth roots in polar form. Question 3(e) worked solution Proving a quotient is purely imaginary from equal moduli.

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Complex-number algebra Polar form and De Moivre

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