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Thought-Process to Discover Knowledge

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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

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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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exercise.

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» Complex Multiplicative inverse of `z` is `1/z`.

→ `z xx 1/(z) = 1`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

• For any complex number `z` there exists `1/z` : multiplicative inverse

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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Complex numbers have multiplicative inverse.

Starting on learning "Multiplicative Inverse". ;; In this page you will learn about multiplicative inverse of a complex number.

What does 'inverse' mean?

- same; identical; similar
- opposite; converse

The answer is 'opposite; converse'.

Consider two complex numbers `z_1 = a+ i b` and `z_2 = 1 /(a+ib)`. What will be `z_1 xx z_2`?

- `1`
- `1+0i`
- multiplicative identity
- All the above

The answer is 'All the above'

Consider two complex numbers `z_1 = a+ i b` and `z_2 = 1 /(a+ib)`.

`z_2 = 1/(a+ib)`

`quad quad quad = 1/(a+ib) xx (a-ib)/(a-ib) `

`quad quad quad = (a-ib)/(a^2+b^2)`

`1/z` or (a-ib)/(a^2+b^2) is the multiplicative inverse.

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

** Multiplicative Inverse: **For any complex number `z = a+ib in CC`, there exists `1/z = (a - i b)/(a^2+b^2) in CC` such that

`z xx 1/z = 1`

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

What is the multiplicative inverse of `2-i`?

- `2+i`
- `(2+i)/5`
- `(2+i)/sqrt(5)`

The answer is '`(2+i)/5`'

*your progress details*

Progress

*About you*

Progress

What does 'inverse' mean?

same;identical;similar

same; identical; similar

opposite;converse

opposite; converse

The answer is 'opposite; converse'.

Consider two complex numbers z1 = a+ i b and z2 = 1 by a+i b. What will be z1 multiplied z2?

1

1

0

1+0i

multiplicative;identity

multiplicative identity

all;above

All the above

The answer is 'All the above'

Consider two complex numbers z1 = a+ i b and z2 = 1 by a+i b. ;; z2 = 1 by a+i b ;; equals 1 by a+ib into a minus i b by a minus i b ;; equals a minus i b by a squared +b squared ;; 1 by z, or a minus i b by a squared +b squared, is the multiplicative inverse.

For any complex number z there exists 1 by z : multiplicative inverse

Multiplicative Inverse: For any complex number z = a+i b in complex numbers, there exists 1 by z = (a minus i b) by a squared plus b squared in complex numbers such that z into 1 by z equals 1.

What is the multiplicative inverse of 2 minus i?

1

2+i

2

2 plus i, by 5

3

2 plus i, by square root of 5

The answer is 2 plus i, by 5