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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.

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User Guide

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The content is presented in small-focused learning units to enable you to
think,
figure-out, &
learn.

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User Guide

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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

### Properties of Complex Number Arithmetic

Voice

Voice

Home

Complex Algebraic Identities

»  All identities of real-numbers holds

→  (a+b)^2 = a^2+2ab+b^2

→  (a-b)^2, etc.

### Algebraic Identities for Complex numbers

plain and simple summary

nub

plain and simple summary

nub

dummy

•  Algebraic identities are same as that of real numbers.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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The algebraic identities of complex number is same as that for real numbers.

Keep tapping on the content to continue learning.
Starting on learning "Algebraic Identities for Complex numbers". ;; In this page you will learn that The algebraic identities of complex number is same as that for real numbers.

Which of the following are examples of algebraic identities?

• (a+b)^2 = a^2+2ab+b^2
• (a-b)^2 = a^2-2ab+b^2
• a^2-b^2 = (a+b)(a-b)
• all the above

The answer is 'all the above'

If an algebraic identity is true for real numbers, will that be true for complex numbers?

• No, it will not be true at all
• Yes, for all identities with four fundamental operations

The answer is 'Yes, for all identities with four fundamental operations'.

The four fundamental operations like
•  addition,
•  subtraction,
•  multiplication, and
•  division define the properties
•  associative,
•  commutative
•  distributive.

The algebraic identities employ the properties of the operations given above. Between real numbers and complex numbers the properties are same. So the algebraic identities will hold true.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Algebraic Identities: (z_1+z_2)^2 = z_1^2+ 2z_1z_2+z_2^2
(z_1-z_2)^2 = z_1^2 - 2z_1z_2+z_2^2
(z_1+z_2)(z_1-z_2) = z_1^2 - z_2^2
(z_1+z_2)^3 = z_1^3+z_2^3+ 3z_1^2z_2+ 3z_1z_2^2
and so on.

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

your progress details

Progress

About you

Progress

Which of the following are examples of algebraic identities?
plus;+
a + b whole squared = a square plus 2 a b + b squared
minus
a minus b whole squared = a squared minus 2 a b + b squared
squared minus;squared -
a squared minus b squared = a + b multiplied a minus b
all;above
all the above
The answer is 'all the above'
If an algebraic identity is true for real numbers, will that be true for complex numbers?
no;not
No, it will not be true at all
s;yes;4;four
Yes, for all identities with four fundamental operations
The answer is 'Yes, for all identities with four fundamental operations'.
The four fundamental operations like ;; addition, subtraction, multiplication, and division ;; define the properties ; associative, commutative, and distributive. ;; The algebraic identities employ the properties of the operations given above. Between real numbers and complex numbers the properties are same. So the algebraic identities will hold true.
Algebraic identities are same as that of real numbers.
Algebraic Identities: z1+z2, squared = z1 squared + 2 z1 z2+z2 squared ;; z1 minus z2 squared = z1 squared minus 2 z1 z2+z2 squared ;; z1+z2 multiplied, z1 minus z2 = z1 squared - z2 squared ;; and so on.

we are not perfect yet...