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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 commutative.

    →  `z_1 + z_2 = z_2 + z_1`

Addition : Commutative Law

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  Complex numbers can be swapped in complex addition - commutative.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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


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 addition.

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 addition and subtraction of complex numbers. `z_3 = z_1+z_2` given as `a_3+ib_3 = (a_1+a_2)+i(b_1+b_2)`, where `a_1, a_2, b_1, b_2 in RR`.

Will `z_1+z_2 = z_2+z_1`?commutative property illustration

  • Yes, the real and imaginary part addition is nothing but real number addition.
  • No. The properties of complex numbers need to be studied to understand.

The answer is 'Yes, the real and imaginary part addition is nothing but real-number addition.'.

Is commutative property defined for complex subtraction?

  • No. The properties are not defined for inverse operations.
  • Yes. The properties are defined for subtraction too

The answer is 'No. The properties are not defined for inverse operations.' Subtraction is the inverse of addition.

Subtraction is the inverse of addition.

The commutative property has to be used in the following way.
`z_1-z_2`
`quad quad = z_1 + (-z_2)`
`quad quad =(-z_2) + z_1 `(commutative property of addition.)

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

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



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given two complex numbers `z_1, z_2`; `z_1+z_2 = 3.1+i2.9`. Find the value of `z_2+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 addition and subtraction of complex numbers. z3 = z1+z2 given as a3+i b3 =; a1+a2, +i b1+b2, where a1, a2, b1, b2 in real numbers.

Will z1+z2 = z2+z1?
yes;s;real;imaginary
Yes, the real and imaginary part addition is nothing but real number addition.
no;properties;complex
No. The properties of complex numbers need to be studied to understand.
The answer is 'Yes, the real and imaginary part addition is nothing but real-number addition.'.
Complex numbers can be swapped in complex addition - commutative.
Commutative Property of Complex addition: for any complex number z1, z2 in complex numbers ;; z1 + z2 = z2 + z1
Is commutative property defined for complex subtraction?
no;not;inverse
No. The properties are not defined for inverse operations.
s;yes;subtraction
Yes. The properties are defined for subtraction too
The answer is ""
Subtraction is the inverse of addition. ;; The commutative property has to be used in the following way. ;; z1 minus z2 ; equals; z1 + minus z2 ; equals ; minus z2 + z1 ; by commutative property of addition.
Given two complex numbers z1, z2; z1+z2 = 3 point 1+i 2 point 9. Find the value of z2+z1.
1
3 point 1 + i 2 point 9
2
3 point 1 minus i 2 point 9
3
minus 3 point 1 + i 2 point 9
4
2 point 9 + i 3 point 1
The answer is '3 point 1 + i2 point 9

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