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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.
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Add, Subtract, Multiply
What is it?
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.
In simple words
- 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.
Important terms
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.
What you should learn
- 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.
Examples
- (1+2i)+(3-i)=4+i
- (2+i)(3-i)=7+i
- i * i = -1
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.
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.
Recommended for Class 11
Full school-level explanation
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.
Understand the idea, then apply it:
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.
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.
Remember
- like with like, then foil
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.
Remember
- focused answer
- accurate support
Examples
- State the central idea
- Use one accurate detail
- Check the final response
How to answer a add, subtract, multiply question
How it works
- 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.
Remember
- like with like, then foil
- z = x + i y
- equal <-> both parts equal
- R inside C
- like with like, then foil
- focused answer
- accurate support
- like with like, then foil
Deeper understanding
Go beyond memorising Add, Subtract, Multiply. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Core Idea
What to Know
Example or Evidence
How to Answer
Exam focus
Quick revision
- like with like, then foil
- z = x + i y
- equal <-> both parts equal
- R inside C
- 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. Foi
- ADD, SUBTRACT, MULTIPLY: Add: (a+bi)+(c+di)=(a+c)+(b+d)i.
Reals are complex numbers with Im = 0. Do not say 'not complex' for 5.
For long answers on Add, Subtract, Multiply: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- like with like, then foil
- z = x + i y
- equal <-> both parts equal
- R inside C
Important formulas
- like with like, then foil
- z = x + i y
- equal <-> both parts equal
Common exam traps
- Reals are complex numbers with Im = 0. Do not say 'not complex' for 5.
- Do not choose a formula before checking that its conditions fit the question.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Reals are complex numbers with Im = 0. Do not say 'not complex' for 5.
- Mistake
Do not choose a formula before checking that its conditions fit the question.
- Mistake
Do not hide sign changes, restrictions, or skipped algebra steps.
- Mistake
Reals are complex numbers with Im = 0. Do not say 'not complex' for 5.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
like with like, then foil
z = x + i y
equal <-> both parts equal
R inside C
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.
z = x + i y
- 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.
- Formula
- z = x + i y
- Example
- (1+2i)+(3-i)=4+i
- Critical warning
- Reals are complex numbers with Im = 0. Do not say 'not complex' for 5.
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Exam Practice
Define
Q1. Define Add, Subtract, Multiply.
Explain
Q2. Explain: MAIN IDEA.
Example
Q3. Give one clear example of Add, Subtract, Multiply and say why it fits.
Mistake
Q4. State one common mistake students make about Add, Subtract, Multiply.
Exam note
Q5. Write a short exam note on Add, Subtract, Multiply: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.