MathematicsChapter 1: Complex Numbers
The Four Values
i^1 = i. i^2 = -1. i^3 = i^2 * i = -i.
Learning objectives
- Define and explain the four values.
- Apply the four values to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
i1 = i. i2 = -1. i3 = i2 * i = -i. i4 = (i2)2 = 1. Then i5 = i again. Negative powers: i-1 = 1i = -i, and i-2 = 1/i2 = -1.
Mathematical form
i = -i. i4
i = -i
Where / symbols
- The Four Values
- i^1 = i. i^2 = -1. i^3 = i^2 * i = -i. i^4 = (i^2)^2 = 1. Then i^5 = i again. Negative powers: i^{-1} = 1/i = -i, and i^{-2} = 1/i^2 = -1.
Relationship
- i2 = -1
Overview
Learn the idea, then use it:
Core Understanding
i1 = i. i2 = -1. i3 = i2 * i = -i. i4 = (i2)2 = 1. Then i5 = i again. Negative powers: i-1 = 1i = -i, and i-2 = 1/i2 = -1.
Examples i, -1, -i, 1 · i^2 = -1 · period 4 · THE FOUR VALUES: i^1 = i. i^2 = -1. i^3 = i^2 * i = -i. i^4 = (i^2)^2 = 1. Then i^5 = i again. Negative powers: i^{-1} = 1/i = -i, and i^
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 — THE FOUR VALUES
i1 = i. i2 = -1. i3 = i2 * i = -i. i4 = (i2)2 = 1. Then i5 = i again. Negative powers: i-1 = 1i = -i, and i-2 = 1/i2 = -1.
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 the four values with a neighbouring idea that uses a different definition, rule, or method.
Key points
- i, -1, -i, 1
- i2 = -1
- period 4
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.The Four Values
Sticky Notes · Quick Revision
Core Idea
- i1 = i.
Key Points
- i, -1, -i, 1
- i2 = -1
- period 4
Simple Check
- Explain the four values 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 the four values 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
- i1 = i.
- i, -1, -i, 1
- i2 = -1
- period 4
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