MathematicsChapter 1: Complex Numbers
Add, Subtract, Multiply
Add: (a+bi)+(c+di)=(a+c)+(b+d)i.
Learning objectives
- State the rule or meaning of add, subtract, multiply in easy words.
- Apply add, subtract, multiply in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Definition
Add: (a+bi)+(c+di)=(a+c)+(b+d)i. Multiply: (a+bi)(c+di) = ac + adi + bci + bdi^2, then i^2 = -1. Foil, then tidy.
Where / symbols
- ADD, SUBTRACT, MULTIPLY
- Add: (a+bi)+(c+di)=(a+c)+(b+d)i. Multiply: (a+bi)(c+di) = ac + adi + bci + bdi^2, then i^2 = -1. Foil, then tidy.
- ADD, SUBTRACT, MULTIPLY
- Add: (a+bi)+(c+di)=(a+c)+(b+d)i.
Relationship
- z = x + i y
Overview
Understand the idea, then apply it:
Main Idea
Add: (a+bi)+(c+di)=(a+c)+(b+d)i. Multiply: (a+bi)(c+di) = ac + adi + bci + bdi^2, then i^2 = -1. Foil, then tidy.
Examples (1+2i)+(3-i)=4+i · (2+i)(3-i)=7+i · i * i = -1
Exam Use
Write the rule first: Add: (a+bi)+(c+di)=(a+c)+(b+d)i. 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 — ADD, SUBTRACT, MULTIPLY
Add: (a+bi)+(c+di)=(a+c)+(b+d)i. Multiply: (a+bi)(c+di) = ac + adi + bci + bdi^2, then i^2 = -1. Foil, then tidy.
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: Add: (a+bi)+(c+di)=(a+c)+(b+d)i. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
How to answer a add, subtract, multiply 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
- like with like, then foil
- 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.Add, Subtract, Multiply
Sticky Notes · Quick Revision
Core Idea
- Add: (a+bi)+(c+di)=(a+c)+(b+d)i.
What to Know
- Add: (a+bi)+(c+di)=(a+c)+(b+d)i. Multiply: (a+bi)(c+di) = ac + adi + bci + bdi^2, then i^2 = -1. Foil, then tidy.
Example or Evidence
- (1+2i)+(3-i)=4+i
- (2+i)(3-i)=7+i
- i * i = -1
How to Answer
- Write the rule first: Add: (a+bi)+(c+di)=(a+c)+(b+d)i. 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
- Add: (a+bi)+(c+di)=(a+c)+(b+d)i.
- (1+2i)+(3-i)=4+i
- (2+i)(3-i)=7+i
- State the rule, show the working, and check the answer.
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.