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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**.

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think,

figure-out, &

learn.

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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.

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» Complex Multiplication is associative.

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

*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.

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`'.

*your progress details*

Progress

*About you*

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'