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summary of this topic

Properties of Complex Number Arithmetic

Properties of Complex Number Arithmetic

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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

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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.

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