NCEA Level 3 Complex Numbers (AS91577)

📘 Course Overview

AS91577: Apply the Algebra of Complex Numbers in Solving Problems.

Master the essential concepts of the Algebra of Complex Numbers.

This course prepares students thoroughly for the NCEA Level 3 external Examination, with structured coverage of all examinable Complex Numbers content. Students develop fluency with the algebra and geometry of complex numbers, including modulus, argument, conjugate, multiplication, polar form, De Moivre’s Theorem, and n-th roots of complex numbers. Strong emphasis is placed on Merit and Excellence-level problem solving, including proof-style questions, higher-order reasoning (HOQs), and multi-step algebraic arguments. The course systematically develops skills required for locus problems, including Cartesian equations, sketching loci, and interpreting argument and modulus conditions. Algebraic techniques such as rationalisation, simplification, and real-complex links (binomial expansions, cubic equations, surd equations) are integrated to reflect external exam demands. By the end of the course, students are fully prepared to interpret, structure, and justify solutions clearly, enabling confident performance in the External Examination, with a strong focus on achieving Merit-Excellence.

Who This Course Is For?

 Students sitting in Level 3 Calculus External Examination

Student Outcomes

Students who complete this course typically:

•  Gain confidence in algebra with complex numbers
•  Improve clarity and accuracy in exam reasoning
•  Learn how to structure answers to meet Merit/Excellence criteria
•  Score higher in the Level 3 external exam