Complex Numbers Polynomials and Rational Functions Training

Learning Outcomes

• Apply algebraic operations (addition, subtraction, multiplication, division) to complex numbers in Cartesian and polar forms.
• Simplify polynomial expressions using factorization, expansion, and the remainder and factor theorems.
• Analyze rational functions by simplifying, performing partial fraction decomposition, and identifying domain restrictions.
• Evaluate complex number expressions involving powers and roots using De Moivre's theorem.
• Demonstrate proficiency in solving equations involving complex numbers, polynomials, and rational functions.
• Translate real-world problems into mathematical statements involving complex numbers, polynomials, or rational functions and solve them.

Target Audience

This course is designed for students, technicians, engineers, and professionals who require a solid grounding in algebraic manipulation of complex numbers, polynomials, and rational functions for further technical or academic study.

Prerequisites

None — open enrollment. However, basic arithmetic and algebra skills are recommended.

Course Outline

Practicals

Overview

The practicals reinforce theoretical concepts through hands-on problem-solving sessions. Learners will work through graded exercises involving complex number calculations, polynomial manipulations, and rational function analysis. These sessions develop procedural fluency and critical thinking skills essential for engineering and science applications.

Practical Activities

• Complex Number Operations and Polar Form — Learners perform arithmetic operations on complex numbers, convert between rectangular and polar forms, and apply De Moivre’s theorem to find powers and roots. (3h)
• Polynomial Division and Factorisation — Learners carry out polynomial long division and synthetic division, apply the Remainder and Factor Theorems, and factorise polynomials completely. (3h)
• Rational Functions and Partial Fractions — Learners simplify rational expressions, identify asymptotes, and decompose proper rational functions into partial fractions. (2h)

Summatives

Each delegate is assessed continuously throughout the course via daily exercises, scored practical assignments, and a final summative test at the end.

Practical Assignments — 30%

Practical assignments are observed and scored against a rubric during the practical sessions. Each delegate's practical mark is averaged into a single 100% score and contributes 30% to the final total.

Daily Exercises — 20%

Every training day ends with a multiple-choice exercise scored out of 100%. The scores from each daily exercise are averaged across the duration of the course to produce a Daily Average mark, which contributes 20% to the final total.

Final Test — 50%

On the last day a final summative test is written. It is a multiple-choice paper with multiple-answer questions: each question may have more than one correct option, and a single wrong selection on a question marks the entire question wrong — no partial credit. The final test is scored out of 100% and contributes 50% to the overall mark.

Final Total

Component	Out of	Weight
Practical Assignments (rubric-scored)	100%	30%
Daily Average (multiple choice)	100%	20%
Final Test (multi-answer multiple choice)	100%	50%
Final Total	—	100%

All marks are recorded on the AATICD LMS and visible to each learner under their account.

Certificate

How it works

• Certificates are auto-generated on the AATICD LMS as soon as the marks pass the 50% threshold.
• Each certificate is a branded PDF with the delegate's name, the course title, the unit standard ID, NQF level, credits, and the date of issue.
• You can download or print your certificate from your LMS dashboard at any time after issue — there's no reissue fee and no expiry date.
• If you scored under 50% you can sit the final test again at the next scheduled session at no extra cost.

Where to find it

Sign in to the LMS, open your dashboard, and your certificates appear under My Certificates. Each entry has a View / Download button and a print option.

Training Discounts

Group discounts apply automatically — the more delegates you enrol, the greater the saving. Discounts are calculated at 3% per 5 delegates, scaling up to 40% off for 100+ delegates.

Delegates	Discount
5	3% off
10	6% off
15	9% off
20	12% off
25	15% off
30	18% off
50	30% off
75	35% off
100	40% off

3% discount per 5 delegates, up to 40% off for 100+ delegates. Contact us for a custom group quote.