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Technical Mathematics Grade 12 | VirtualX MasterClass – Course Module 1 introduces learners to Complex Numbers, a fundamental concept in advanced mathematics. This module builds on Grade 11 knowledge and focuses on operations with complex numbers, their geometric representation, and their applications in real-world technical and engineering problems.
Through interactive lessons, problem-solving activities, and real-world applications, students will develop analytical skills crucial for engineering, physics, and advanced mathematics.
By the end of this module, learners will be able to:
• Perform operations on complex numbers (addition, subtraction, multiplication, division).
• Understand and apply the concept of complex conjugates.
• Graph complex numbers using the Argand diagram.
• Compute and interpret modulus and argument.
• Convert between Cartesian and polar forms of complex numbers.
This course consists of six structured lessons, each focusing on essential concepts in Complex Numbers.
Lesson 1: Revision of Grade 11 Complex Numbers
- Definition and structure of complex numbers: z = a + bi
- Real and imaginary components
- Complex conjugates and their significance
- Operations: Addition, subtraction, multiplication, division
- Introduction to the Argand diagram
Lesson 2: Definition and Basic Operations
- Understanding imaginary unit i (i² = -1)
- Adding and subtracting complex numbers
- Multiplication and division of complex numbers
- Applying basic operations to solve equations
Lesson 3: Complex Conjugates
- Definition and properties of complex conjugates
- Applications in division of complex numbers
- Using conjugates in simplifying expressions
- Real-world applications in electrical engineering and physics
Lesson 4: Argand Diagram Representation
- Plotting complex numbers on the Argand plane
- Real and imaginary axes interpretation
- Distance from the origin (modulus)
- Rotational representation of complex numbers
Lesson 5: Argument and Modulus
- Definition of modulus (magnitude) of a complex number: |z| = sqrt(a² + b²)
- Definition of argument (angle) θ = tan⁻¹(b/a)
- Finding modulus and argument for various complex numbers
- Applications in trigonometry and wave functions
Lesson 6: Polar and Trigonometric Forms
- Conversion between Cartesian (a + bi) and Polar (r(cosθ + i sinθ)) forms
- Euler’s formula: e^(iθ) = cosθ + i sinθ
- Applications in electrical engineering and physics
- Practical problem-solving using different forms of complex numbers
Each lesson includes interactive exercises, quizzes, problem-solving scenarios, and assessments to reinforce understanding and ensure mastery of complex numbers.
Course Currilcum
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- Lesson 1: Revision of Grade 11 Complex Numbers Unlimited