ADV009 · Advanced mathematics · Classes 11–12
Complex number operations
Complex numbers add like vectors and multiply using i² = −1. Multiplying multiplies the moduli and adds the arguments.
z₁ z₂Complex number operations
📐 Formula
(a + bi)(c + di) = (ac − bd) + (ad + bc)i
✏️ Worked example
(1 + 2i)(3 − i) = 3 − i + 6i − 2i² = 5 + 5i; sum 4 + i.
🌍 Where it is used
Rotations and scaling in 2D graphics; circuit analysis.
❓ Quick check
i² = ?
🏋️ Practice
Easy(2 + i) + (1 − 3i)?
Answer: 3 − 2i
Medium(1 + i)²?
Answer: 2i
Challenge(3 + 4i)(3 − 4i)?
Answer: 25