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Thought-Process to Discover Knowledge

Welcome to nubtrek.

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 commutative.

→  z_1 xx z_2 = z_2 xx z_1

### Multiplication : Commutative Law

plain and simple summary

nub

plain and simple summary

nub

dummy

•  Complex numbers can be swapped in complex multiplication - commutative

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Complex multiplication is commutative : Complex numbers can be swapped in complex multiplication.

Keep tapping on the content to continue learning.
Starting on learning "commutative law of complex numbers". ;; In this page, you will learn that complex numbers can be swapped in complex multiplication.

What does 'commute' mean?

• to go to and fro on a regular basis
• It is not an English word.

The answer is 'to go to and fro between two places on a regular basis'.

Consider the multiplication and division of complex numbers. z_3 = z_1 xx z_2 given as a_3+ib_3 = (a_1a_2-b_1b_2)+i(a_2b_1+a_1b_2), where a_1, a_2, b_1, b_2 in RR.

Will z_1 xx z_2 = z_2 xx z_1?

• Yes. If one interchanges a_1 and a_2 ; b_1 and b_2, the result is the same
• No. If one interchanges a_1 and a_2 ; b_1 and b_2, the result is different.

The answer is 'Yes. If I interchange a_1 and a_2 ; b_1 and b_2, the result is same'

Is commutative property defined for complex division?

• No. Commutative property is not defined for inverse operations.
• Yes. Commutative property is defined for division

The answer is 'No. Commutative property is not defined for inverse operations.' Division is the inverse of multiplication.

Division is the inverse of multiplication.

The commutative property has to be used in the following way.
z_1-:z_2
quad quad = z_1 xx (1/z_2)
quad quad =(1/z_2) xx z_1 (commutative property of multiplication)

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Commutative Property of Complex Multiplication: for any complex number z_1, z_2 in CC
z_1 xx z_2 = z_2 xx z_1

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given for two complex numbers z_1, z_2; z_1 xx z_2 = 3.1+i2.9. Find the value of z_2 xx z_1.

• 3.1+i2.9
• 3.1-i2.9
• -3.1+i2.9
• 2.9+i3.1

The answer is '3.1+i2.9'

Progress

Progress

What does 'commute' mean?
go;to;fro;regular;basis
to go to and fro on a regular basis
not;English;word
It is not an English word.
The answer is 'to go to and fro between two places on a regular basis'.
Consider the multiplication and division of complex numbers. z3 = z1 multiplied z2, given as a3+i b3 = a1 a2 minus b1 b2+i, a2 b1+a1 b2, where a1, a2, b1, b2 in real numbers . ;; Will z1 multiplied z2 = z2 multiplied z1?
yes;s;same
Yes. If one interchanges a1 and a2 ; b1 and b2, the result is the same
no;different
No. If one interchanges a1 and a2 ; b1 and b2, the result is different.
The answer is 'Yes. If one interchanges a1 and a2 ; b1 and b2, the result is the same'
Complex numbers can be swapped in complex multiplication - commutative
Is commutative property defined for complex division?
no;not;inverse
No. Commutative property is not defined for inverse operations.
yes;s;division
Yes. Commutative property is defined for division
The answer is 'No. Commutative property is not defined for inverse operations.' Division is the inverse of multiplication.
Division is the inverse of multiplication. ;; The commutative property has to be used in the following way. ;; z1 divided by z2 <;; equals z1 multiplied 1 by z2;; equals 1 by z2 multiplied z1, by commutative property of multiplication
Commutative Property of Complex Multiplication: for any complex number z1, z2 in complex numbers z1 multiplied z2 = z2 multiplied z1
Given for two complex numbers z1, z2; z1 multiplied z2 = 3 point 1+i 2 point 9. Find the value of z2 multipled z1.
1
3 point 1 plus i 2 point 9
2
3 point 1 minus i 2 point 9
3
minus 3 point 1 plus i 2 point 9
4
2 point 9 plus i 3 point 1
The answer is '3 point 1 plus i 2 point 9'

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