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summary of this topic

Properties of Complex Number Arithmetic

Properties of Complex Number Arithmetic

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 »  Complex Addition is associative.

    →  `z_1 + (z_2 +z_3) = (z_1+z_2)+z_3`

Addition : Associative Law

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  Order of addition can be changed - associative.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Complex addition is associative : Order of addition can be changed.


Keep tapping on the content to continue learning.
Starting on learning "Associative Law". ;; In this page you will learn that order of addition can be change.

What does 'Associate' mean?Associative property illustration

  • to connect with; to join
  • to separate

The answer is 'to connect with; to join'

When three complex numbers are added,
 •  Person A associates the middle complex number with first complex number and, to the result of that, he adds the third complex number `(z_1 + z_2) + z_3`
 •  Person B associates the middle complex number with third complex number and to that she adds the first complex number `z_1 + (z_2+z_3)`

will the two persons get different results?

  • They will get different results.
  • They will get identical results

The answer is 'They will get identical results'.

Is Associative property applicable to subtraction?

  • when subtraction is handled as inverse of addition.
  • yes. Order of subtraction can be swapped

The answer is 'when subtraction is handled as inverse of addition'. For `(z_1 - z_2) - z_3`, it will be considered as `(z_1 + (-z_2)) + (-z_3)`.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Associative Property of Complex Addition: For Any complex number `z_1,z_2,z_3 in CC`,
`z_1+(z_2+z_3) = (z_1+z_2)+z_3`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given `z_1, z_2 in CC`, what will be the result of `z_1 + z_2 + z_1`?

  • `2z_1+z_2`
  • `z_1+z_2`
  • `z_2`
  • `z_1+2z_2`

The answer is '`2z_1+z_2`'.

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Progress

What does 'Associate' mean?
connect;join
to connect with; to join
separate
to separate
The answer is 'to connect with; to join'
When three complex numbers are added,;; Person A associates the middle complex number with first complex number and, to the result of that, he adds the third complex number z1 + z2, + z3 ;; Person B associates the middle complex number with third complex number and to that she adds the first complex number z1 +, z2+z3 ; will the two persons get different results?
different
They will get different results.
identical
They will get identical results
The answer is 'They will get identical results'.
Order of addition can be changed - associative.
Associative Property of Complex Addition: For Any complex number z1,z2,z3 in complex numbers, z1+z2, +z3 = z1+, z2+z3
Is Associative property applicable to subtraction?
handled;inverse;addition
when subtraction is handled as inverse of addition.
yes;s;order
yes. Order of subtraction can be swapped
The answer is 'when subtraction is handled as inverse of addition'. For z1 minus z2, minus z3, it will be considered as z1 +, minus z2 + minus z3
Given z1, z2 in complex numbers, what will be the result of z1 + z2 + z1 ?
2 z1;2z1
2 z1 + z2
z1+z2
z1 + z2
z2
z2
2z2
z1+2 z2
The answer is ' 2z1 + z2'.

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