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Properties of Complex Number Arithmetic

Properties of Complex Number Arithmetic

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 »  Complex Multiplication is commutative.

    →  `z_1 xx z_2 = z_2 xx z_1`

Multiplication : Commutative Law

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  Complex numbers can be swapped in complex multiplication - commutative

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Complex multiplication is commutative : Complex numbers can be swapped in complex multiplication.


Keep tapping on the content to continue learning.
Starting on learning "commutative law of complex numbers". ;; In this page, you will learn that complex numbers can be swapped in complex multiplication.

What does 'commute' mean?commutative property illustration

  • to go to and fro on a regular basis
  • It is not an English word.

The answer is 'to go to and fro between two places on a regular basis'.

Consider the multiplication and division of complex numbers. `z_3 = z_1 xx z_2` given as `a_3+ib_3 = (a_1a_2-b_1b_2)+i(a_2b_1+a_1b_2)`, where `a_1, a_2, b_1, b_2 in RR`.

Will `z_1 xx z_2 = z_2 xx z_1`?

  • Yes. If one interchanges `a_1` and `a_2` ; `b_1` and `b_2`, the result is the same
  • No. If one interchanges `a_1` and `a_2` ; `b_1` and `b_2`, the result is different.

The answer is 'Yes. If I interchange `a_1` and `a_2` ; `b_1` and `b_2`, the result is same'

Is commutative property defined for complex division?

  • No. Commutative property is not defined for inverse operations.
  • Yes. Commutative property is defined for division

The answer is 'No. Commutative property is not defined for inverse operations.' Division is the inverse of multiplication.

Division is the inverse of multiplication.

The commutative property has to be used in the following way.
`z_1-:z_2`
`quad quad = z_1 xx (1/z_2)`
`quad quad =(1/z_2) xx z_1 (commutative property of multiplication)`

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Commutative Property of Complex Multiplication: for any complex number `z_1, z_2 in CC`
`z_1 xx z_2 = z_2 xx z_1`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given for two complex numbers `z_1, z_2`; `z_1 xx z_2 = 3.1+i2.9`. Find the value of `z_2 xx z_1`.

  • `3.1+i2.9`
  • `3.1-i2.9`
  • `-3.1+i2.9`
  • `2.9+i3.1`

The answer is '`3.1+i2.9`'

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What does 'commute' mean?
go;to;fro;regular;basis
to go to and fro on a regular basis
not;English;word
It is not an English word.
The answer is 'to go to and fro between two places on a regular basis'.
Consider the multiplication and division of complex numbers. z3 = z1 multiplied z2, given as a3+i b3 = a1 a2 minus b1 b2+i, a2 b1+a1 b2, where a1, a2, b1, b2 in real numbers . ;; Will z1 multiplied z2 = z2 multiplied z1?
yes;s;same
Yes. If one interchanges a1 and a2 ; b1 and b2, the result is the same
no;different
No. If one interchanges a1 and a2 ; b1 and b2, the result is different.
The answer is 'Yes. If one interchanges a1 and a2 ; b1 and b2, the result is the same'
Complex numbers can be swapped in complex multiplication - commutative
Is commutative property defined for complex division?
no;not;inverse
No. Commutative property is not defined for inverse operations.
yes;s;division
Yes. Commutative property is defined for division
The answer is 'No. Commutative property is not defined for inverse operations.' Division is the inverse of multiplication.
Division is the inverse of multiplication. ;; The commutative property has to be used in the following way. ;; z1 divided by z2 <;; equals z1 multiplied 1 by z2;; equals 1 by z2 multiplied z1, by commutative property of multiplication
Commutative Property of Complex Multiplication: for any complex number z1, z2 in complex numbers z1 multiplied z2 = z2 multiplied z1
Given for two complex numbers z1, z2; z1 multiplied z2 = 3 point 1+i 2 point 9. Find the value of z2 multipled z1.
1
3 point 1 plus i 2 point 9
2
3 point 1 minus i 2 point 9
3
minus 3 point 1 plus i 2 point 9
4
2 point 9 plus i 3 point 1
The answer is '3 point 1 plus i 2 point 9'

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