MathematicsChapter 1: Complex Numbers
Check
If you claim (2+3i)(1+i) = -1+5i, expand the left again.
Learning objectives
- Define and explain check.
- Apply check to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
If you claim (2+3i)(1+i) = -1+5i, expand the left again. If you claim a quotient is i, multiply i by the old denominator and compare with the numerator.
Where / symbols
- Check
- If you claim (2+3i)(1+i) = -1+5i, expand the left again. If you claim a quotient is i, multiply i by the old denominator and compare with the numerator.
Overview
Learn the idea, then use it:
Core Understanding
If you claim (2+3i)(1+i) = -1+5i, expand the left again. If you claim a quotient is i, multiply i by the old denominator and compare with the numerator.
Examples multiply back · a + bi finished · check by reverse · CHECK: If you claim (2+3i)(1+i) = -1+5i, expand the left again. If you claim a quotient is i, multiply i by the old denominator
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 — CHECK
If you claim (2+3i)(1+i) = -1+5i, expand the left again. If you claim a quotient is i, multiply i by the old denominator and compare with the numerator.
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 check with a neighbouring idea that uses a different definition, rule, or method.
Key points
- multiply back
- a + bi finished
- check by reverse
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Check
Sticky Notes · Quick Revision
Core Idea
- If you claim (2+3i)(1+i) = -1+5i, expand the left again.
Key Points
- multiply back
- a + bi finished
- check by reverse
Simple Check
- Explain check 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 check 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
- If you claim (2+3i)(1+i) = -1+5i, expand the left again.
- multiply back
- a + bi finished
- check by reverse
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