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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.

User Guide

Welcome to nubtrek.

The content is presented in small-focused learning units to enable you to
think,
figure-out, &
learn.

Just keep tapping (or clicking) on the content to continue in the trail and learn.

User Guide

To make best use of nubtrek, understand what is available.

nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

nub,

trek,

jogger,

exercise.

User Guide

nub is the simple explanation of the concept.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about.

User Guide

trek is the step by step exploration of the concept.

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step.

User Guide

jogger provides the complete mathematical definition of the concepts.

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen.

User Guide

exercise provides practice problems to become fluent in the concepts.

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge.

summary of this topic

### Properties of Complex Number Arithmetic

Voice

Voice

Home

»  Complex Multiplication is associative.

→  z_1 xx (z_2 xx z_3) = (z_1 xx z_2) xx z_3

### Multiplication : Associative Law

plain and simple summary

nub

plain and simple summary

nub

dummy

•  Order of multiplication can be changed - associative

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Complex multiplication is associative : Order of multiplication can be changed.

Keep tapping on the content to continue learning.
Starting on learning "Associative law of multiplication". ;; In this page you will learn that the order of multiplication can be changed.

What does 'Associate' mean?

• to connect with; to join
• to separate

The answer is 'to connect with; to join'

When three complex numbers are multiplies,
•  Person A associates the middle complex number with first complex number and, to the result of that, he multiplies the third complex number (z_1 xx z_2) xx z_3
•  Person B associates the middle complex number with third complex number and to that she multiplies the first complex number z_1 xx (z_2 xx z_3) will the two persons get different results?

• They will get different results.
• They will get identical results

The answer is 'They will get identical results'.

Is Associative property applicable to division?

• when Division is handled as inverse of multiplication.
• Order of division can be swapped

The answer is 'when Division is handled as inverse of multiplication'. For (z_1 -: z_2) -: z_3, it will be handled (z_1 xx 1/z_2)xx 1/z_3, then associative property of multiplication applies.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Associative property of Complex Multiplication: For Any complex number z_1,z_2,z_3 in CC,
z_1 xx (z_2 xx z_3) = (z_1 xx z_2) xx z_3

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given z_1, z_2 in CC, what will be the result of z_1 xx (z_2 xx z_1)?

• z_1^2 xx z_2
• z_1 xx z_2
• z_2

The answer is 'z_1^2 xx z_2'.

Progress

Progress

What does 'Associate' mean?
connect;join
to connect with; to join
separate
to separate
The answer is 'to connect with; to join'
When three complex numbers are multiplies,;; Person A associates the middle complex number with first complex number and, to the result of that, he multiplies the third complex number z1 into z2, into z3 ;; Person B associates the middle complex number with third complex number and to that she multiplies the first complex number z1 into, z2 into z3 ;; will the two persons get different results?
different
They will get different results.
identical
They will get identical results
The answer is 'They will get identical results'.
Order of multiplication can be changed - associative.
Associative property of Complex Multiplication: For Any complex number z1,z2,z3 in complex numbers, z1 into z2, into z3 = z1 into, z2 into z3
Is Associative property applicable to division?
handled;inverse;multiplication
when Division is handled as inverse of multiplication.
order;can;swapped
Order of division can be swapped
The answer is 'when Division is handled as inverse of multiplication'. For z1 by z2, by z3, it will be handled z1 into 1 by z2, into 1 by z3 ;;then associative property of multiplication applies.
Given z1, z2 in complex numbers, what will be the result of z1 into, z2 into z1?
squared
z1 squared into z2
into
z1 into z2
z2
z2
The answer is 'z1 squared into z2'

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