All Modules
Grade 11 Math Lab: Transcendence & Limits FREE
Loading simulation...
Complex Numbers
Learning Objectives
- Perform arithmetic with complex numbers
- Graph on complex plane
- Find modulus and argument
Key Concepts
Imaginary Unit
i = √(-1), i² = -1
Complex Number
a + bi where a is real part, b is imaginary part
Theory
**Complex number:** z = a + bi
**Operations:**
- Add/Sub: Combine like parts
- Multiply: FOIL, use i² = -1
- Conjugate: z̄ = a - bi
- Divide: Multiply by conjugate
**Modulus:** |z| = √(a² + b²)
**Argument:** θ = arctan(b/a)
**Polar form:** z = r(cosθ + i·sinθ) = r·e^(iθ)
Examples
(3 + 2i)(1 - i)
Solution: 3 - 3i + 2i - 2i² = 3 - i + 2 = 5 - i