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Thought-Process to Discover Knowledge

Welcome to nubtrek.

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.

User Guide

Welcome to nubtrek.

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.

User Guide

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.

User Guide

nub is the simple explanation of the concept.

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

User Guide

trek is the step by step exploration of the concept.

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.

User Guide

jogger provides the complete mathematical definition of the concepts.

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.

User Guide

exercise provides practice problems to become fluent in the concepts.

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.

summary of this topic

### Algebra of Complex Numbers

Voice

Voice

Home

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

### Powers of i

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

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

Keep tapping on the content to continue learning.
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'

Progress

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
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
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