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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 closed: Sum or difference of two complex numbers is another complex number.



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What does 'closure' mean?closure property illustration

  • closed
  • not open
  • both the above
  • both the above

Answer is 'both the above'

What is the "span" mean?

  • Full extent of something; all that is included in that;
  • Full extent of something; all that is included in that;
  • past tense of spin

The answer is 'Full extent of something'

What is the span of complex numbers?

  • `a+ib` with `a,b in RR`
  • real and imaginary parts taking any real number
  • both the above
  • both the above

The answer is 'Both the above'

The span of complex numbers or the set of complex numbers is represented as `CC`.

When any two complex numbers are added will it result in a number within the span of complex numbers?

  • Yes. It will be another complex number.
  • Yes. It will be another complex number.
  • No. It extends the complex numbers to something beyond the set of complex numbers.

The answer is 'Yes. It will be another complex number'

 •  Sum or difference of two complex numbers is another complex number - closure property

Closure Property of Addition and Subtraction: For any given complex numbers `z_1, z_2 in CC`, ` z_1 +- z_2 in CC`.

Solved Exercise Problem:

Given a complex number `z` and `a`. What will be the sum `z+a`?

  • a real number
  • a complex number
  • a complex number
  • addition between a complex number and real number is not defined

The answer is 'a complex number'

                            
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