Quadratic Equations and Complex Numbers
Learning Time: 5-15 hours
Content: Quadratic equations and complex numbers is the subject that examines the solutions of second degree polynomials and the complex number system. The 2025 curriculum includes the root formula, discriminant analysis, complex numbers (i = √-1) and basic operations. The emphasis is on basic equations in TYT, while the emphasis is on complex numbers and advanced applications in AYT.
- Basic Concepts:
- 2. Definition of Degree Equation (ax² + bx + c = 0, a ≠ 0)
- Discriminant (Δ = b² – 4ac) and the Nature of Roots
- Root Formula (x = [-b ± √Δ] / 2a)
- Solution Techniques:
- Factoring Method
- Perfect Square Technique
- Number of Roots (Real, Equal, Imaginary)
- Advanced Calculus (AYT):
- Complex Numbers (z = a + bi)
- Conjugate (z̅ = a – bi) and Module (|z| = √(a² + b²))
- Basic Operations (Addition, Multiplication, Division)
- Applications:
- Physical Models (Parabolic Motion)
- Use of Complex Numbers in Engineering
- Daily Life Examples (Optimization Problems)
- Affecting Factors:
- Discriminant Value (Δ)
- Type of Coefficients (Real/Complex)
- Complexity of Roots
Course Features
- Lectures 0
- Quizzes 0
- Duration 5 hours
- Skill level Expert
- Language English
- Students 15
- Assessments Yes
