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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.

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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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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.

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» Complex Multiplication is commutative.

→ `z_1 xx z_2 = z_2 xx z_1`

*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*

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

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`'

*your progress details*

Progress

*About you*

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'