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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 closed.

→  z_1 xx z_2 in CC

### Multiplication : Closure Law

plain and simple summary

nub

plain and simple summary

nub

dummy

•  Product or quotient of two complex number is another complex number - closed

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Complex multiplication is closed : Product or quotient of two complex number is another complex number

Keep tapping on the content to continue learning.
Starting on learning "Closure law of multiplication". ;; In this page you will learn that the product or quotient of two complex numbers is another complex number.

What does 'closure' mean?

• closed
• not open
• both the above

Given complex numbers z_1=a_1+b_1i and z_2=a_2+b_2i, a_1,a_2,b_1,b_2 in R, will z_1 xx z_2 a complex number?

• No. When multiplied, the result has i^2
• Yes. When multiplied, the result consists of real numbers, as real and imaginary parts

The answer is 'Yes. When multiplied, the result consists of real numbers as real and imaginary parts'

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Closure property of Multiplication and Division: For any given complex numbers z_1, z_2 in CC,  z_1 xx / -: z_2 in CC.

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given complex numbers z_1=a_1+b_1i and z_2=a_2+b_2i, a_1,a_2,b_1,b_2 in R, will z_1 -: z_2 a complex number?

• No. Complex division is not defined
• Yes. complex number division is equivalently multiplication by the conjugate

The answer is 'Yes. When multiplied, the result consists of real numbers as real and imaginary parts'

Progress

Progress

What does 'closure' mean?
closed;close
closed
not;open
not open
both;above
both the above
Given complex numbers z1=a1+b1 i and z2=a2+b2 i, a1,a2,b1,b2 in real numbers, will z1 multiplied by z2 a complex number?
no;has;i;squared
No. When multiplied, the result has i squared
yes;s;consists;real;imaginary
Yes. When multiplied, the result consists of real numbers, as real and imaginary parts
The answer is 'Yes. When multiplied, the result consists of real numbers as real and imaginary parts'
Product or quotient of two complex number is another complex number - closed
Closure property of Multiplication and Division: For any given complex numbers z1, z2 in complex numbers, z1 multiplied or divided by z2 is a complex number
Given complex numbers z1=a1+b1 i and z2=a2+b2 i, a1,a2,b1,b2 in real numbers, will z1 divided by z2 a complex number?
no;not;defined
No. Complex division is not defined
yes;equivalently;multiplication;conjugate
Yes. complex number division is equivalently multiplication by the conjugate
The answer is 'Yes. When multiplied, the result consists of real numbers as real and imaginary parts'

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