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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

→  z_1 + z_2 in CC

plain and simple summary

nub

plain and simple summary

nub

dummy

•  Sum or difference of two complex numbers is another complex number - closure property

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Complex addition is closed: Sum or difference of two complex numbers is another complex number.

Keep tapping on the content to continue learning.
Starting on learning "Closure Law of addition". ;; In this page, you will learn that Sum or difference of two complex numbers is another complex number.

What does 'closure' mean?

• closed
• not open
• both the above

What is the "span" mean?

• Full extent of something; all that is included in that;
• past tense of spin

The answer is 'Full extent of something'

What is the span of complex numbers?

• a+ib with a,b in RR
• real and imaginary parts taking any real number
• both the above

The answer is 'Both the above'

The span of complex numbers or the set of complex numbers is represented as CC.

When any two complex numbers are added will it result in a number within the span of complex numbers?

• Yes. It will be another complex number.
• No. It extends the complex numbers to something beyond the set of complex numbers.

The answer is 'Yes. It will be another complex number'

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Closure Property of Addition and Subtraction: For any given complex numbers z_1, z_2 in CC,  z_1 +- z_2 in CC.

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given a complex number z and a. What will be the sum z+a?

• a real number
• a complex number
• addition between a complex number and real number is not defined

The answer is 'a complex number'

Progress

Progress

What does 'closure' mean?
closed;close
closed
not;open
not open
both;above
both the above
What is the "span" mean?
full;extent;something
Full extent of something; all that is included in that;
past;tense;spin
past tense of spin
The answer is 'Full extent of something'
What is the span of complex numbers?
a;plus;i;b
a + i b with a, b in real numbers
real;imaginary
real and imaginary parts taking any real number
both;above
both the above
The answer is 'Both the above'
The span of complex numbers or the set of complex numbers is represented as C.
When any two complex numbers are added will it result in a number within the span of complex numbers?
yes;s;will;another
Yes. It will be another complex number.
no;extends;beyond
No. It extends the complex numbers to something beyond the set of complex numbers.
The answer is 'Yes. It will be another complex number'
Sum or difference of two complex numbers is another complex number - closure property
Closure Property of Addition and Subtraction: For any given complex numbers z1, z2, ; z1 plus or minus z2 is in complex numbers.
Given a complex number z and a . What will be the sum z+a ?
real
a real number
complex
a complex number