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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 numbers have an additive identity 0.



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What does "identical" mean?

  • exactly alike; same in every detail
  • exactly alike; same in every detail
  • different; mismatched

The answer is "exactly alike; same in every detail"

Consider the complex number `0+i0`. What will be the result of adding that with a complex number `z_1`?

  • `0+i0`
  • `z_1`
  • `z_1`

The answer is '`z_1`'. The sum is identical to the complex number being added.

What is an additive identity?

  • an element, when added, will result in sum identical to the addend.
  • an element, when added, will result in sum identical to the addend.
  • the phrase "additive identity" does not have any meaning.

The answer is 'an element, when added, will result in sum identical to the addend.'.

 •  `0 = 0+i0` is additive identity.

Additive Identity in complex numbers: For any complex number `z_1 in CC`, there exists `0 = 0+i0, 0 in CC` such that
`z_1 + 0 = z_1`

Solved Exercise Problem:

Consider `z_1 = e+ pi i `. What will be the sum `z_1 + 0`?

  • `z_1`
  • `e+pi i`
  • both the above
  • both the above

The answer is 'Both the above'

                            
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