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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.

**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

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Power of i

» To calculate `i^n`*Remember `i^4 = 1` and `i^2=-1`. Quickly derive the following using this. No need to memorize*

→ express `n` in the form `n=4p+2q+r`, where `p,q, r in NN` natural numbers.

→ `i^n = (-1)^q xx i^r`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

To calculate `i^n`, use `i^4=1` and `i^2=-1`.

*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.

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The value of `i^n` for various values of n is discussed.

Starting on learning "Powers of i". ;;The value of i power n for various values of n is discussed.

What is the value of `i`?

- `-1`
- `sqrt(-1)`

The answer is '`sqrt(-1)`'

What is the value of `i^2`?

- `-1`
- `sqrt(-1)`

The answer is '`-1`'

It is defined that `i=sqrt(-1)`. Substitute that in the following

`i^2`

`quad quad = (sqrt(-1))^2`

`quad quad = (-1^(1/2))^2`

`quad quad = -1^(2/2)`

`quad quad = -1`

What is the value of `i^3`?

- `-1`
- `i`
- `-i`

The answer is '`-i`'

`i^3`

`quad quad = i^(2+1)`

`quad quad = i^2 xx i^1`

`quad quad = -1 xx i`

`quad quad = -i`

What is the value of `i^4`?

- `1`
- `-1`

The answer is '`1`'

`i^4`

`quad quad = i^(2+2)`

`quad quad = (i)^2 xx i^2`

`quad quad = -1 xx -1`

`quad quad = 1`

What is the value of `i^0`?

- `1`
- `-1`
- `i`

The answer is '`1`'

`i^0`

`quad quad = i^(1-1)`

`quad quad = i/i`

`quad quad = 1`

What is the value of `i^n`, if `n=4p+2q+r`?

- `i`
- `(-1)^q xx i^r`
- `i^r`

The answer is '`(-1)^q xx i^r`'

`i^n`

`quad quad = i^(4p+2q+r)`

`quad quad = i^(4p) xx i^(2q) xx i^r`

`quad quad = (i^4)^p) xx (i^2)^q) xx i^r`

`quad quad = (-1)^q xx i^r`

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Power of i:** To calculate `i^n`, express `n` in the form `n=4p+2q+r`, where `p,q, r in NN` natural numbers. Then

`i^n = (-1)^q xx i^r`.

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

What is the value of `i^27`?

- `1`
- `-i`
- `i`

The answer is '`-i`'

What is `i^20`?

- `1`
- `-1`
- `i`
- `-i`

The answer is '`1`'

What is `i^7`?

- `1`
- `-1`
- `i`
- `-i`

The answer is '`-i`'

*your progress details*

Progress

*About you*

Progress

What is the value of i ?

minus 1;-1

minus 1

square;root

square root of minus 1

The answer is 'square root of minus 1'

What is the value of i squared?

minus 1;-1

minus 1

square;root

square root of minus 1

The answer is ' -1 '

What is the value of i cube?

minus 1;-1

minus 1

i

i

minus i;-i

minus i

The answer is 'minus i'

What is the value of i power 4?

1

1

-1;minus 1

minus 1

The answer is ' 1 '

What is the value of i power 0?

1

1

-1;minus 1

minus 1

i

i

The answer is ' 1 '

What is the value of i power n if n equals 4p+2q+r?

i

i

minus

minus 1 power q multiplied i power r

i;power;r;are;or

i power r

The answer is 'minus 1 power q multiplied i power r'

To calculate i power n, use i power 4 equals 1 and i squared equals minus 1

Power of i: To calculate i power n, express n in the form 4p+2q+r, where p,q, r in whole numbers. Then ;; i power n = minus 1 power q multiplied by i power r .

What is the value of i power 27?

1

1

minus i

minus i

i

i

The answer is 'minus i'

What is the value of i power 20?

1

1

minus 1

minus 1

i

i

minus i

minus i

The answer is ' 1 '

What is i power 7?

1

1

minus 1

minus 1

i

i

minus i

minus i

The answer is 'minus i'