Server Not Reachable. *This may be due to your internet connection or the nubtrek server is offline.*

Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

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.continue

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.continue

Welcome to **nub****trek**.

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. continue

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

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.

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

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. continue

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. continue

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. continue

Voice

Voice

Home

» Complex Multiplication is closed.

→ `z_1 xx z_2 in CC`

*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

You are learning the free content, however do shake hands with a coffee to show appreciation.

*To stop this message from appearing, please choose an option and make a payment.*

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

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

Answer is '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'

*your progress details*

Progress

*About you*

Progress

What does 'closure' mean?

closed;close

closed

not;open

not open

both;above

both the above

Answer is '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