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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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



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What does 'commute' mean?commutative property illustration

  • to go to and fro on a regular basis
  • 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.
  • 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.'.

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

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

Is commutative property defined for complex subtraction?

  • No. The properties are not defined for inverse operations.
  • 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.)

Solved Exercise Problem:

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`
  • `-3.1+i2.9`
  • `2.9+i3.1`

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

                            
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