6 min read
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 = 1i2 = -1.
Choose Your Level
The Four Values
What is it?
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 = 1i2 = -1.
In simple words
- i1 = i.
- i, -1, -i, 1
- i2 = -1
- period 4
Important terms
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 = 1i2 = -1.
What you should learn
- 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.
Examples
- i, -1, -i, 1
- i2 = -1
- period 4
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 = 1i2 = -1.
EXAM APPLICATION
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Recommended for Class 10
Full school-level explanation
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 = 1i2 = -1.
Learn the idea, then use it:
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 = 1i2 = -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.
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 = 1i2 = -1.
Remember
- i, -1, -i, 1
- i2 = -1
- period 4
Examples
- i, -1, -i, 1
- i2 = -1
- period 4
- 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
EXAM APPLICATION
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Remember
- correct term
- chapter link
- clear application
Examples
- Define first
- Show the rule or evidence
- Check units, labels, and conclusion
Remember
- i, -1, -i, 1
- i2 = -1
- period 4
- keep the ideas separate
- i, -1, -i, 1
- i2 = -1
- period 4
- correct term
Deeper understanding
Go beyond memorising The Four Values. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Core Idea
Key Points
Simple Check
How to Answer
Exam focus
Quick revision
- i, -1, -i, 1
- i2 = -1
- period 4
- keep the ideas separate
- The Four Values: i1 = i. i2 = -1. i3 = i2 * i = -i. i4 = (i2)2 = 1. Then i5 = i again. Negative powers: i-1
- WHAT — THE FOUR VALUES: i1 = i. i2 = -1. i3 = i2 * i = -i. i4 = (i2)2 = 1. Then i5 = i again. Negative powers: i-1
Do not merge the four values with a neighbouring idea that uses a different definition, rule, or method.
For long answers on The Four Values: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- i, -1, -i, 1
- i2 = -1
- period 4
- keep the ideas separate
Important formulas
- i, -1, -i, 1
- i2 = -1
- period 4
Common exam traps
- Do not merge the four values with a neighbouring idea that uses a different definition, rule, or method.
- Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not merge the four values with a neighbouring idea that uses a different definition, rule, or method.
- Mistake
Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
- Mistake
Do not merge the four values with a neighbouring idea that uses a different definition, rule, or method.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
i, -1, -i, 1
i2 = -1
period 4
keep the ideas separate
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 = 1i2 = -1.
i2 = -1
- 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 = 1i2 = -1.
- Formula
- i2 = -1
- Example
- i, -1, -i, 1
- Critical warning
- Do not merge the four values with a neighbouring idea that uses a different definition, rule, or method.
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.
Ready to test yourself?
You've completed the learning section.
Exam Practice
Define
Q1. Define The Four Values.
Explain
Q2. Explain: CORE UNDERSTANDING.
Example
Q3. Give one clear example of The Four Values and say why it fits.
Mistake
Q4. State one common mistake students make about The Four Values.
Exam note
Q5. Write a short exam note on The Four Values: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.