MathematicsChapter 1: Complex Numbers
Name the Parts
Re(z) = x. Im(z) = y.
Learning objectives
- State the rule or meaning of name the parts in easy words.
- Apply name the parts in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Definition
Re(z) = x. Im(z) = y. Pure imaginary: x = 0, y != 0. Real: y = 0. 0 = 0 + 0i is still in C. Powers of i cycle every 4 (i, -1, -i, 1).
Mathematical form
x = 0
y = 0. 0
Where / symbols
- NAME THE PARTS
- Re(z) = x. Im(z) = y. Pure imaginary: x = 0, y != 0. Real: y = 0. 0 = 0 + 0i is still in C. Powers of i cycle every 4 (i, -1, -i, 1).
- NAME THE PARTS
- Re(z) = x.
Relationship
- z = x + i y
Overview
Understand the idea, then apply it:
Main Idea
Re(z) = x. Im(z) = y. Pure imaginary: x = 0, y != 0. Real: y = 0. 0 = 0 + 0i is still in C. Powers of i cycle every 4 (i, -1, -i, 1).
Examples 3 + 2i · 7i pure imaginary · i^2 = -1
Exam Use
Write the rule first: Re(z) = x. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Examples State the central idea · Use one accurate detail · Check the final response
WHAT — NAME THE PARTS
Re(z) = x. Im(z) = y. Pure imaginary: x = 0, y != 0. Real: y = 0. 0 = 0 + 0i is still in C. Powers of i cycle every 4 (i, -1, -i, 1).
WHY — Why it matters
This rule is a separate learning unit inside complex numbers recalled. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: Re(z) = x. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
How to answer a name the parts question
- Read the exact command word and identify what the question asks.
- State the matching idea, rule, or meaning before adding detail.
- Use the unit evidence or mathematical working that directly supports the answer.
- Check accuracy, relevance, and answer length before finishing.
In simple words
Reals are complex numbers with Im = 0. Do not say 'not complex' for 5.
Key points
- Re and Im
- z = x + i y
- equal <-> both parts equal
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Name the Parts
Sticky Notes · Quick Revision
Core Idea
- Re(z) = x.
What to Know
- Re(z) = x. Im(z) = y. Pure imaginary: x = 0, y != 0. Real: y = 0. 0 = 0 + 0i is still in C. Powers of i cycle every 4 (i, -1, -i, 1).
Example or Evidence
- 3 + 2i
- 7i pure imaginary
- i2 = -1
How to Answer
- Write the rule first: Re(z) = x. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Common Error
- Reals are complex numbers with Im = 0. Do not say 'not complex' for 5.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- Re(z) = x.
- 3 + 2i
- 7i pure imaginary
- State the rule, show the working, and check the answer.
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