lightbulb Key Concepts

< div id = "study-notes" style = "background: rgba(255,255,255,0.03); padding: 1.5rem; border-radius: 12px; border: 1px solid rgba(255,255,255,0.1); margin-bottom: 2rem; line-height: 1.6;" >

1. Imaginary Unit i

The unit i is defined as √-1, such that i² = -1, i³ = -i, i⁴ = 1.

2. Standard Form

A complex number is written as z = a + bi, where a is the real part and b is the imaginary part.

3. Operations

• Modulus: |z| = √(a² + b²)
• Conjugate: z̄ = a - bi
• Addition: (a + bi) + (c + di) = (a+c) + (b+d)i

Multiplication uses the FOIL method and substitute i² = -1.