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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**.

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

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.

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

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» Complex Addition is commutative.

→ `z_1 + z_2 = z_2 + z_1`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

• Complex numbers can be swapped in complex addition - commutative.

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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

Starting on learning "Commutative law of complex numbers". ;; In this page, you will learn that Complex numbers can be swapped in complex addition.

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 addition and subtraction of complex numbers. `z_3 = z_1+z_2` given as `a_3+ib_3 = (a_1+a_2)+i(b_1+b_2)`, where `a_1, a_2, b_1, b_2 in RR`.

Will `z_1+z_2 = z_2+z_1`?

- Yes, the real and imaginary part addition is nothing but real number addition.
- No. The properties of complex numbers need to be studied to understand.

The answer is 'Yes, the real and imaginary part addition is nothing but real-number addition.'.

Is commutative property defined for complex subtraction?

- No. The properties are not defined for inverse operations.
- Yes. The properties are defined for subtraction too

The answer is 'No. The properties are not defined for inverse operations.' Subtraction is the inverse of addition.

Subtraction is the inverse of addition.

The commutative property has to be used in the following way.

`z_1-z_2`

`quad quad = z_1 + (-z_2)`

`quad quad =(-z_2) + z_1 `(commutative property of addition.)

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

** Commutative Property of Complex addition: ** for any complex number `z_1, z_2 in CC`

`z_1 + z_2 = z_2 + z_1`

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

Given two complex numbers `z_1, z_2`; `z_1+z_2 = 3.1+i2.9`. Find the value of `z_2+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 addition and subtraction of complex numbers. z3 = z1+z2 given as a3+i b3 =; a1+a2, +i b1+b2, where a1, a2, b1, b2 in real numbers.

Will z1+z2 = z2+z1?

Will z1+z2 = z2+z1?

yes;s;real;imaginary

Yes, the real and imaginary part addition is nothing but real number addition.

no;properties;complex

No. The properties of complex numbers need to be studied to understand.

The answer is 'Yes, the real and imaginary part addition is nothing but real-number addition.'.

Complex numbers can be swapped in complex addition - commutative.

Commutative Property of Complex addition: for any complex number z1, z2 in complex numbers ;; z1 + z2 = z2 + z1

Is commutative property defined for complex subtraction?

no;not;inverse

No. The properties are not defined for inverse operations.

s;yes;subtraction

Yes. The properties are defined for subtraction too

The answer is ""

Subtraction is the inverse of addition. ;; The commutative property has to be used in the following way. ;; z1 minus z2 ; equals; z1 + minus z2 ; equals ; minus z2 + z1 ; by commutative property of addition.

Given two complex numbers z1, z2; z1+z2 = 3 point 1+i 2 point 9. Find the value of z2+z1.

1

3 point 1 + i 2 point 9

2

3 point 1 minus i 2 point 9

3

minus 3 point 1 + i 2 point 9

4

2 point 9 + i 3 point 1

The answer is '3 point 1 + i2 point 9