ADV007 · Advanced mathematics · Classes 11–12
Complex number modulus
The modulus |z| of z = a + bi is its distance from the origin.
|z|Complex number modulus
📐 Formula
|a + bi| = √(a² + b²); z z̄ = |z|²
✏️ Worked example
|4 − 3i| = √(16 + 9) = 5.
🌍 Where it is used
Amplitude of signals and AC voltages.
❓ Quick check
|5 + 12i| = ?
🏋️ Practice
Easy|3i|?
Answer: 3
Medium|1 + i|?
Answer: √2
Challenge|z z̄| for z = 2 + i?
Answer: 5