MathematicsChapter 1: Complex Numbers
Multiplicative Inverse of A Complex Number
z * (1/z) = 1. If z = x+iy, 1/z = (x-iy)/(x^2+y^2).
Learning objectives
- State the rule or meaning of multiplicative inverse of a complex number in easy words.
- Apply multiplicative inverse of a complex number in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Definition
z * (1z) = 1. If z = x+iy, 1z = x-iyx2+y2. Useful in linear systems with complex coefficients.
Mathematical form
z = x+iy
z = x-iyx2+y2. Useful in linear syste
Where / symbols
- MULTIPLICATIVE INVERSE OF A COMPLEX NUMBER
- z * (1/z) = 1. If z = x+iy, 1/z = (x-iy)/(x^2+y^2). Useful in linear systems with complex coefficients.
- INVERSE
- z * (1/z) = 1.
Relationship
- z != 0
- 1z = z-bar / |z|2
Overview
Understand the idea, then apply it:
Main Idea
z * (1z) = 1. If z = x+iy, 1z = x-iyx2+y2. Useful in linear systems with complex coefficients.
Examples 1/i = -i · 1/(1+i) = (1-i)/2 · |z|^2 in the bottom
Exam Use
Write the rule first: z * (1z) = 1. 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 — MULTIPLICATIVE INVERSE OF A COMPLEX NUMBER
z * (1z) = 1. If z = x+iy, 1z = x-iyx2+y2. Useful in linear systems with complex coefficients.
WHY — Why it matters
This rule is a separate learning unit inside division and the inverse. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: z * (1z) = 1. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
How to answer a multiplicative inverse of a complex number 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
If the denominator is 0, the quotient is not defined. Check |w| first.
Key points
- z != 0
- multiply by conjugate of the bottom
- 1z = z-bar / |z|2
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Multiplicative Inverse of A Complex Number
Sticky Notes · Quick Revision
Core Idea
- z * (1z) = 1.
What to Know
- z * (1z) = 1. If z = x+iy, 1z = x-iyx2+y2. Useful in linear systems with complex coefficients.
Example or Evidence
- 1i = -i
- 11+i = 1-i2
- |z|^2 in the bottom
How to Answer
- Write the rule first: z * (1z) = 1. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Common Error
- If the denominator is 0, the quotient is not defined. Check |w| first.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- z * (1z) = 1.
- 1i = -i
- 11+i = 1-i2
- 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.