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Properties of Complex Number Arithmetic

Properties of Complex Number Arithmetic

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 »  Complex Multiplication is associative.

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

Multiplication : Associative Law

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  Order of multiplication can be changed - associative

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trek

simple steps to build the foundation

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


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

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 multiplies,
 •  Person A associates the middle complex number with first complex number and, to the result of that, he multiplies the third complex number `(z_1 xx z_2) xx z_3`
 •  Person B associates the middle complex number with third complex number and to that she multiplies the first complex number `z_1 xx (z_2 xx z_3)` Associative property illustration 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 division?

  • when Division is handled as inverse of multiplication.
  • Order of division can be swapped

The answer is 'when Division is handled as inverse of multiplication'. For `(z_1 -: z_2) -: z_3`, it will be handled `(z_1 xx 1/z_2)xx 1/z_3`, then associative property of multiplication applies.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Associative property of Complex Multiplication: For Any complex number `z_1,z_2,z_3 in CC`,
`z_1 xx (z_2 xx z_3) = (z_1 xx z_2) xx 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 xx (z_2 xx z_1)`?

  • `z_1^2 xx z_2`
  • `z_1 xx z_2`
  • `z_2`

The answer is '`z_1^2 xx z_2`'.

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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 multiplies,;; Person A associates the middle complex number with first complex number and, to the result of that, he multiplies the third complex number z1 into z2, into z3 ;; Person B associates the middle complex number with third complex number and to that she multiplies the first complex number z1 into, z2 into 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 multiplication can be changed - associative.
Associative property of Complex Multiplication: For Any complex number z1,z2,z3 in complex numbers, z1 into z2, into z3 = z1 into, z2 into z3
Is Associative property applicable to division?
handled;inverse;multiplication
when Division is handled as inverse of multiplication.
order;can;swapped
Order of division can be swapped
The answer is 'when Division is handled as inverse of multiplication'. For z1 by z2, by z3, it will be handled z1 into 1 by z2, into 1 by z3 ;;then associative property of multiplication applies.
Given z1, z2 in complex numbers, what will be the result of z1 into, z2 into z1?
squared
z1 squared into z2
into
z1 into z2
z2
z2
The answer is 'z1 squared into z2'

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