MathematicsChapter 1: Complex Numbers
Modulus
|3+4i| = 5 because 9+16=25.
Learning objectives
- Define and explain modulus.
- Apply modulus to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
|3+4i| = 5 because 9+16=25. |-5+12i| = 13. |z| is never negative. |z| = 0 only at the origin 0+0i.
Where / symbols
- Modulus
- |3+4i| = 5 because 9+16=25. |-5+12i| = 13. |z| is never negative. |z| = 0 only at the origin 0+0i.
Relationship
- |z| = sqrt(a2+b2)
Overview
Learn the idea, then use it:
Core Understanding
|3+4i| = 5 because 9+16=25. |-5+12i| = 13. |z| is never negative. |z| = 0 only at the origin 0+0i.
Examples sqrt of sum of squares · conjugate flips b · |z| = sqrt(a^2+b^2) · MODULUS: |3+4i| = 5 because 9+16=25. |-5+12i| = 13. |z| is never negative. |z| = 0 only at the origin 0+0i.
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
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 the result.
In simple words
Do not merge modulus with a neighbouring idea that uses a different definition, rule, or method.
Key points
- sqrt of sum of squares
- conjugate flips b
- |z| = sqrt(a2+b2)
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Modulus
Sticky Notes · Quick Revision
Core Idea
- |3+4i| = 5 because 9+16=25.
Key Points
- sqrt of sum of squares
- conjugate flips b
- |z| = sqrt(a2+b2)
Simple Check
- Explain modulus in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge modulus with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- |3+4i| = 5 because 9+16=25.
- sqrt of sum of squares
- conjugate flips b
- |z| = sqrt(a2+b2)
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