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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 associative : Order of addition can be changed.



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What does 'Associate' mean?Associative property illustration

  • to connect with; to join
  • 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
  • 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 `z_1,z_2,z_3 in CC`,
`z_1+(z_2+z_3) = (z_1+z_2)+z_3`

Is Associative property applicable to subtraction?

  • when subtraction is handled as inverse of addition.
  • 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)`.

Solved Exercise Problem:

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

  • `2z_1+z_2`
  • `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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