Topic explanation

Standard explanation

|3+4i| = 5 because 9+16=25. |-5+12i| = 13. |z| is never negative. |z| = 0 only at the origin 0+0i.

Key points

• sqrt of sum of squares
• conjugate flips b
• |z| = sqrt(a²+b²)
• keep the ideas separate
• Modulus: |3+4i| = 5 because 9+16=25. |-5+12i| = 13. |z| is never negative. |z| = 0 only at the origin 0+0i.
• WHAT — MODULUS: |3+4i| = 5 because 9+16=25. |-5+12i| = 13. |z| is never negative. |z| = 0 only at the origin 0+0i.
• HOW — Use the idea: Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check
• CORE UNDERSTANDING: |3+4i| = 5 because 9+16=25. |-5+12i| = 13. |z| is never negative. |z| = 0 only at the origin 0+0i.

Labelled diagram